Integer Exponents

Videos, examples, solutions, and lessons to help Grade 8 students know and apply the properties of integer exponents to generate equivalent numerical expressions.
For example, 3 2 × 3 –5 = 3 –3 = 1/3 3 = 1/27.

Common Core: 8.EE.1

Suggested Learning Targets

• I can explain why a zero exponent produces a value of one.
• I can explain how a number raised to an exponent of -1 is the reciprocal of that number.
• I can explain the properties of integer exponents to generate equivalent numerical expressions.

1. Multiplying Exponents of the same base
For example, 3 2 x 3 -5 = 1/3 3 = 1/27

2. Dividing Exponents of the same base
For example, 3 2 / 3 -1 = 1/3 3 = 1/27

Applying exponents rules
Examples:
Apply the rules to the problems:
1. (10 5 )(10 3 ) =
2. 3x 7 •5x 4 =
3. (a 2 )(a 5 )(a 4 ) =
4. (y -7 )(y 5 ) =

Divide the following, leaving the answers with exponents.
1. 5 6 ÷ 5 2
2. 8 7 /8 3

Simplify and perform the operation indicated.
1. 2 3 × 3 2
2. 6 2 ÷ 2 3

Simplify and perform the operation indicated.
1. 3 2 + 2 3
2. 5 2 + 3 3
3. 4 2 + 9 3
4. 2 3 - 2 2

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