g-03: zero and negative exponents warm-up: simplify each ... · zero exponent rule: any term (or...

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G-03: Zero and Negative Exponents

Warm-Up: Simplify each of the following exponential expressions.

1. 5𝑥2𝑥4 2. (4𝑚5)5

3. (3𝑥𝑧5)3 4. 3𝑥4

𝑥3

5. (−4𝑥3)(−5𝑥7) 6. 3𝑥𝑦6

12𝑦4𝑥

7. −15𝑎2𝑏2

−3𝑎𝑏 8. (4𝑥2𝑦2)3(2𝑦5)

Investigation: Complete the table below using a calculator. Express all numbers as a fraction, not a

decimal.

Values for n → 3 2 1 0 -1 -2 -3

2n 23 = 8 22 = 4 21 = 2 20 = 1 2-1 =

1

2 2-2 = 2-3 =

3n

4n

5n

Post-Table Questions:

1. Compare the values of 23 and 2-3, 22 and 2-2, and 21 and 2-1. What conclusions can you make

about negative exponents?

2.Compare the values of 20, 30, 40, and 50. What conclusions can you make about zero exponents?

Zero Exponent Rule: Any term (or group of terms) being raised to the zero exponent is equal to _____.

Why?

Examples:

1. 𝑎0 = 2. (𝑥3)0 =

3, (3𝑥4)2(2𝑦)0= 4.

Negative Exponent Rule: Any term (or group of terms) being raised to a negative exponent in the

numerator move to the denominator and change to a positive exponent. Any term (or group of

terms) being raised to a negative exponent in the denominator move to the numerator and change

to a positive exponent.

Why?

Examples:

5. (10𝑥5𝑦3)−3 6. 𝑥−1𝑦

𝑥𝑦−2

0

2

2513

53

5

zyx

7. 2𝑥2𝑦

−6𝑥𝑦−1 8.

20𝑥−3𝑦9

5𝑥−2𝑦−2

9. (2𝑥−1𝑦5

𝑥3𝑦−2)−3