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**NS2. 1 Understand negative whole-number exponents**

NS2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base. AF2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that include exponents. California Standards

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**Additional Example 1: Using a Pattern to Evaluate Negative Exponents**

Simplify the powers of 10. A. 10–2 10–2 = 1 10 • 10 = 1 100 = 0.01 Multiply. Write as a decimal. B. 10–1 10 = –1 1 10 = = 0.1 1 10 Multiply. Write as a decimal.

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**10–8 10–8 = = Multiply. Write as a decimal. Check It Out! Example 1A**

Simplify the powers of 10. 10–8 10–8 = 1 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 = 1 100,000,000 Multiply. = Write as a decimal.

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**Extend the pattern from Example 1A.**

Check It Out! Example 1B Simplify the powers of 10. 10–9 Extend the pattern from Example 1A. 10–9 = 1 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 = 1 1,000,000,000 Multiply. = Write as a decimal.

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NEGATIVE EXPONENTS

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**Additional Example 2A: Evaluating Negative Exponents**

Simplify. 5–3 Write the power under 1; change the sign of the exponent. 1 5 • 5 • 5 = Find the product. 125 1 = Simplify.

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**Additional Example 2B: Evaluating Negative Exponents**

Simplify. (–10)–3 Write the power under 1; change the sign of the exponent. 1 –10 • –10 • –10 = Find the product. –1000 1 = = –0.001 Simplify.

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**Simplify. 4–2 Check It Out! Example 2A**

Write the power under 1; change the sign of the exponent. 1 4 • 4 = Find the product. 16 1 = Simplify.

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**Simplify. (–7)–4 Check It Out! Example 2B**

Write the power under 1; change the sign of the exponent. 1 –7 • –7 • –7 • –7 = Find the product. 2401 1 = Simplify.

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**Additional Example 3: Using the Order of Operations**

Simplify 5 – (6 – 4)–3 + (–2)0. 5 – (6 – 4)–3 + (–2)0 5 – (2)–3 + (–2)0 Subtract inside the parentheses. 5 – 1 23 Rewrite 2-3. 5 – 1 8 Simplify the powers. 5 7 8 Add and subtract from left to right.

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