(meaning of n 2n and laws of exponents) · meaning of an (n 2 n) and laws of exponents n;m 2n —...

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Meaning of an (n ∈ N) and Laws of Exponents

an (n ∈ N)의뜻과지수법칙(Meaning of an (n ∈ N) and Laws of Exponents)

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여

an = a× · · · × a︸ ︷︷ ︸n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여a

n = a× · · · × a︸ ︷︷ ︸n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an

= a× · · · × a︸ ︷︷ ︸n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an =

a× · · · × a︸ ︷︷ ︸n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an =

a× · · · × a︸ ︷︷ ︸n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a

× · · · × a︸ ︷︷ ︸n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a×

· · · × a︸ ︷︷ ︸n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · ·

× a︸ ︷︷ ︸n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · ×

a︸ ︷︷ ︸n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a

︸ ︷︷ ︸n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

a

n × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an

× am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an ×

am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × a

m = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am

= an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am =

an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = a

n+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an

+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+

m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)

n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n

= anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n =

anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = a

nbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = an

bn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anb

n

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(a

n)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)

m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m

= anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m =

anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = a

nm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = an

m(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm

(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm

(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(b

(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)

(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n

=an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

bn

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an

÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷

am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am

=

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m

, if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if

n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m

1 , if n = m1

am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1

, if n = m1

am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if

n = m1

am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n

, if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if

n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

n,m ∈ N에대하여an = a× · · · × a︸ ︷︷ ︸

n

an × am = an+m

(ab)n = anbn

(an)m = anm(ab

)n=

an

bn

an ÷ am =

an−m , if n > m1 , if n = m

1am−n , if n < m

Min Eun Gi : https://min7014.github.io

Meaning of an (n ∈ N) and Laws of Exponents

Github:https://min7014.github.io/math20200228005.html

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Min Eun Gi : https://min7014.github.io

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