1. Simplify (– 3x)2. ANSWER 9x2 2. Simplify . a3 2b 5 ANSWER a5 32b5

3. The order of magnitude of Earth’s mass is about 1027 grams 3. The order of magnitude of Earth’s mass is about 1027 grams. The order of magnitude of the sun’s mass is about 1033 grams. About how many times as great is the sun’s mass as Earth’s mass? ANSWER about 106

Use definition of zero and negative exponents EXAMPLE 1 Use definition of zero and negative exponents 1 32 = a. 3– 2 Definition of negative exponents 1 9 = Evaluate exponent. b. (–7)0 = 1 Definition of zero exponent

Use definition of zero and negative exponents EXAMPLE 1 Use definition of zero and negative exponents 5 –2 1 c. = 1 5 2 Definition of negative exponents 1 25 = Evaluate exponent. = 25 Simplify by multiplying numerator and denominator by 25. 1 0 5 (Undefined) = d. 0 – 5 a – n is defined only for a nonzero number a.

GUIDED PRACTICE for Example 1 Evaluate the expression. 2 3 1. 1 2 3. –3 = 1 = 8 2. (–8) – 2 1 64 = 4. (–1 )0 = 1

Evaluate exponential expressions EXAMPLE 2 Evaluate exponential expressions a. 6– 4 64 = 6– 4 + 4 Product of a power property = 60 Add exponents. = 1 Definition of zero exponent

Evaluate exponential expressions EXAMPLE 2 Evaluate exponential expressions b. (4– 2)2 = 4– 2 ∙ 2 Power of a power property = 4– 4 Multiply exponents. 1 4 = Definition of negative exponents 1 256 = Evaluate power. c. 1 3– 4 = 34 Definition of negative exponents = 81 Evaluate power.

Evaluate exponential expressions EXAMPLE 2 Evaluate exponential expressions d. 5– 1 52 = 5– 1 – 2 Quotient of powers property = 5– 3 Subtract exponents. 1 53 = Definition of negative exponents 1 125 = Evaluate power.

GUIDED PRACTICE for Example 2 Evaluate the expression. 5. 1 4– 3 = 64 7. (– 3 ) (– 3 ) – 5 5 = 1 8. 6– 2 62 1 1296 = 6. (5– 3) – 1 = 125

Use properties of exponents EXAMPLE 3 Use properties of exponents Simplify the expression. Write your answer using only positive exponents. a. (2xy–5)3 = 23 x3 (y–5)3 Power of a product property = 8 x3 y–15 Power of a power property = y15 8x3 Definition of negative exponents

Use properties of exponents EXAMPLE 3 Use properties of exponents (2x)–2y5 –4x2y2 b. y5 (2x)2(–4x2y2) = Definition of negative exponents y5 (4x)2(–4x2y2) = Power of a product property y5 –16x4y2 = Product of powers property y3 16x4 – = Quotient of powers property

EXAMPLE 4 Standardized Test Practice The order of magnitude of the mass of a polyphemus moth larva when it hatches is 10-3 gram. During the first 56 days of its life, the moth larva can eat about 105 times its own mass in food. About how many grams of food can the moth larva eat during its first 56 days? A 10–15 gram B 0.00000001 gram C 100 grams D 10,000,000 grams

EXAMPLE 4 Standardized Test Practice SOLUTION To find the amount of food the moth larva can eat in the first 56 days of its life, multiply its original mass, 10– 3, by 105. 105 10–3 = 105 + (–3) = 102 = 100 The moth larva can eat about 100 grams of food in the first 56 days of its life. ANSWER The correct answer is C. A B C D

GUIDED PRACTICE for Examples 3 and 4 9x3y 3xy – 3 9. Simplify the expression . Write your answer using only positive exponents. 1 3x2y4 ANSWER 10. SCIENCE The order of magnitude of the mass of a proton is 104 times greater than the order of magnitude of the mass of an electron, which is 10–27 gram. Find the order of magnitude of the mass of a proton. ANSWER 10 –23 g