evaluating algebraic expressions 4-2 integer exponents ns2.1 understand negative whole-number...
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Evaluating Algebraic Expressions
4-2 Integer 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
Evaluating Algebraic Expressions
4-2 Integer ExponentsAdditional Example 1: Using a Pattern to Evaluate
Negative ExponentsSimplify the powers of 10.
A. 10–2
10–2 = 1
10 • 10
= 1100
= 0.01
B. 10–1
= = 0.1 110
10 =
–1 110
Multiply. Write as a decimal.
Multiply. Write as a decimal.
Evaluating Algebraic Expressions
4-2 Integer ExponentsCheck It Out! Example 1A
Simplify the powers of 10.
10–8
=1
100,000,000
10–8 = 1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
= 0.00000001
Multiply.
Write as a decimal.
Evaluating Algebraic Expressions
4-2 Integer ExponentsCheck It Out! Example 1B
10–9
= 11,000,000,000
10–9 =1
10 • 10 • 10 • 10 • 10 • 10 • 10 • 10 • 10
Extend the pattern from Example 1A.
= 0.000000001
Multiply.
Write as a decimal.
Simplify the powers of 10.
Evaluating Algebraic Expressions
4-2 Integer Exponents
NEGATIVE EXPONENTS
Evaluating Algebraic Expressions
4-2 Integer Exponents
5–3
Write the power under 1; change the sign of the exponent.
Additional Example 2A: Evaluating Negative Exponents
Simplify.
Find the product.
Simplify.
15 • 5 • 5
=
1251
=
Evaluating Algebraic Expressions
4-2 Integer Exponents
(–10)–3
Write the power under 1; change the sign of the exponent.
Additional Example 2B: Evaluating Negative Exponents
Simplify.
Find the product.
Simplify.
1–10 • –10 • –10
=
–1000 1
= = –0.001
Evaluating Algebraic Expressions
4-2 Integer Exponents
4–2
Write the power under 1; change the sign of the exponent.
Check It Out! Example 2A
Simplify.
Find the product.
Simplify.
14 • 4
=
161
=
Evaluating Algebraic Expressions
4-2 Integer Exponents
(–7)–4
Write the power under 1; change the sign of the exponent.
Check It Out! Example 2B
Simplify.
Find the product.
Simplify.
1
–7 • –7 • –7 • –7 =
2401 1
=
Evaluating Algebraic Expressions
4-2 Integer Exponents
Evaluating Algebraic Expressions
4-2 Integer Exponents
Subtract inside the parentheses.
Simplify 5 – (6 – 4)–3 + (–2)0.
Rewrite 2-3.
Additional Example 3: Using the Order of Operations
5 – (6 – 4)–3 + (–2)0
5 – (2)–3 + (–2)0
5 7 8
Add and subtract from left to right.
5 – + 1 1 23
Simplify the powers. 5 – + 1 1 8