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Math 10
4.3 Rational Exponents
Recall the exponent laws:
Multiplying powers with the same base (am )(an) = am+n
Dividing powers with the same base am rn-n= aan
A Power Raised to a Power (amt = am"n
Power of a Quotient u. n an=b bn
Power of a Product (ab)" = an'bn
Zero Exponent aO= 1
We use these SAME laws when working with RATIONAL EXPONENTS.
What is a rational number?
- A number that can be expressed as a fraction (~ ) where a and bare
integers; and b is not equal to zero, • t::: .5. 5e~..__:...J) ) ---- I' >
\ 8- -=rIntegers
- ~.\-/l 0 ~i" 1,+2..i:::- ~ .,.
Rational Numbers:
(all integers, repeating decimals,terminating decimalsl ~ repe«-f)~.~) /.,Jj .) L
Irrational Numbers
A power with a rational exponent can be written as:~-;)...., ~ O.~
.s. .. L1
, Lr )~ \+rCLL-\-)on d~l;!Y\t\ \
x
\- '1
r Ilor~ ---
Quick Review of Operations with Fractions:
Multiplying fractions: . <..)1.. ~ 3e:« ~ ~ Y- -z: --
5-4 '>0"j..
Dividing fractions: (multiply by reciprocal)
" ------------
(find common denominator)
doe-s no\ 9 e:-\ ~J,
9 - \4® \~
''N~\f\) orvrUS0
-fD '( exfl\ ttw S . Adding and Subtracting fractions:
Ct)\Y\ yY\O\l def I ~ac
~
+hc\'~ WLtf\ l(}.A V\V,( Gt~
'f7X.poy\.(n\:S .More Examples of Rational Exponentsrz-. 1-\ Ou5 3'1-0.5
(4X3rv= 1" X
Decimal Fraction0.25 \--
\ . ~~\ 0.5 -L
d-0.75 3---q=-1.5 .z,
o:
Going Between Decimals and Fractions
3
Word Problem:
The bacterium Lactobacillus bulgaricus is used to make yoghurt and cheese. Thegrowth of 10 000 bacteria can be modeled by the formula:
r""ou~ .N = 10000 (2)h/42
, I
5' Cty-\- ~I'\ hWhere N is the number of bacteria after h hours.
a) What does the value 2 in the formula tell you?
::l --k\\s ~OlA ~L ba.L-KnOc oI.CMbk.J Clt'--Ur-L\-'~ "'0\,\ (S.
b) How many bacteria are present after 42 hours?
N -:: \ (J 000 ('J. ')~;}...\
-\ 0 000 ( ~ ')N ~\ ~o aDO]
c) How many bacteria are present after 105 hours?
'~()j DOO blle,.\e.( ~o: ~~r42- n~'
N ~ \0 600 (~)~ta 5
<:: \0 bOO (2-) .
co.\tM~· [=- \0 000 ill J. IE1 ~. 5]
~ \}565 b8 · S l\- 1b(k-\t~Ct a:.\'4u" 4:l- hrs
Do 4.2 Questions: Rational Exponents
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