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**Evaluate numerical expressions**

EXAMPLE 1 Evaluate numerical expressions a. (– )2 = (– 4)2 (25)2 Power of a product property = Power of a power property = = 16,384 Simplify and evaluate power. b. 115 118 –1 118 115 = Negative exponent property = 118 – 5 Quotient of powers property = 113 = 1331 Simplify and evaluate power.

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**Use scientific notation in real life**

EXAMPLE 2 Use scientific notation in real life A swarm of locusts may contain as many as 85 million locusts per square kilometer and cover an area of 1200 square kilometers. About how many locusts are in such a swarm? Locusts SOLUTION = 85,000, Substitute values.

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**Use scientific notation in real life**

EXAMPLE 2 Use scientific notation in real life = ( )( ) Write in scientific notation. = ( )( ) Use multiplication properties. = Product of powers property = Write 10.2 in scientific notation. = Product of powers property The number of locusts is about , or about 102,000,000,000. ANSWER

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**Evaluate the expression. Tell which properties of exponents you used.**

GUIDED PRACTICE for Examples 1 and 2 Evaluate the expression. Tell which properties of exponents you used. (42 )3 SOLUTION (42 )3 = 42 3 Power of a power property = 4096 Simplify and evaluate power.

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**GUIDED PRACTICE for Examples 1 and 2 2. (–8)(–8)3 SOLUTION (–8)(–8)3**

2. (–8)(–8)3 SOLUTION (–8)(–8)3 = (–8)(–8)3 Product of a powers property = (–8)(–512) Multiply = 4096 Simplify

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**GUIDED PRACTICE for Examples 1 and 2 2 3 3. 9 SOLUTION 2 3 23 = 9 93 8**

2 3 9 SOLUTION 2 3 9 23 93 = Power of a quotient property 8 729 = Simplify and evaluate power.

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**GUIDED PRACTICE for Examples 1 and 2 6 10 – 4 9 107 4. SOLUTION**

– 4 4. SOLUTION – 4 6 9 • 10 – 4 – 7 = quotient of power property 6 9 = • 10 – 11 add power 2 3 = • 10 – 11 Negative exponent property 2 = Negative exponent property

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EXAMPLE 1 Evaluate numerical expressions a. (– 4 2 5 ) 2 = 16 2 5 2 Power of a product property Power of a power property Simplify and evaluate power.

EXAMPLE 1 Evaluate numerical expressions a. (– 4 2 5 ) 2 = 16 2 5 2 Power of a product property Power of a power property Simplify and evaluate power.

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