Integer Exponent Properties Guide
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Integer Exponent Properties Guide
Exponent rule control panel
In these rules, a is nonzero and m and n are integers. The product and quotient rules require the same nonzero base.
Same base multiplied: aᵐ × aⁿ = aᵐ⁺ⁿ
Same base divided: aᵐ ÷ aⁿ = aᵐ⁻ⁿ
Power raised to a power: (aᵐ)ⁿ = aᵐⁿ
Zero exponent: a⁰ = 1
Negative exponent: a⁻ⁿ = 1/aⁿ
A negative exponent does not make the value negative; it means take the reciprocal.
Warm-up: choose the rule
Read each expression carefully. The base stays the same in the product and quotient rules.
- Product rule
- Quotient rule
- Power rule
- Zero exponent rule
- −5³
- 1/5³
- 5³
- −15
Code check: simplify each expression
Apply the exponent rules. Give positive-exponent answers when possible.
Debug the tricky expressions
Show how you use the rules. Remember that parentheses tell you which power is raised.
3 printable pages
Page 1
Page 2
Page 3
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