g-03: zero and negative exponents warm-up: simplify each ... · zero exponent rule: any term (or...
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Name _______________________________________________ Date ________________ Hour _____________
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