Laws of exponentsAll three rules
Name: Date:
Write each one as a single power. Give the exponent n.
1(9¹)³ = 9n, n =
2(2¹)⁵ = 2n, n =
311⁸ ÷ 11¹ = 11n, n =
412⁷ ÷ 12¹³ = 12n, n =
512⁹ × 12⁵ = 12n, n =
611¹¹ ÷ 11¹¹ = 11n, n =
- Free
- Grade 8
- Bases 2–9, negative and zero exponents
Laws of exponents worksheets
Three rules, one question each time: two powers of the same base go in and one comes out. These free printable worksheets ask for the exponent, so every answer is a whole number.
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Ready to printLaws of exponents
The answer key prints on a separate page.
What's on this sheet
Asking for the exponent rather than the value is what makes these sheets about the rule. 3² × 3⁴ = 729 is a multiplication a child can do without ever meeting the law, and it cannot ask the two questions the standard is really about: 3² ÷ 3⁵ and 3⁵ ÷ 3⁵ have answers of 1/27 and 1, and neither says anything about exponents. Written as 3ⁿ, both are answerable and both teach the thing.
Why this sheet works
That is why the dividing sheet is the one to spend time on. It is the only one here where the answer can come out negative or zero, and those are not awkward cases to be filtered out — they are where negative and zero exponents come from. Cancel three 3s against seven and four are left underneath, which is what 3⁻⁴ means. Cancel five against five and nothing is left but 1, which is why 3⁰ = 1.
How this one works
One question from this sheet, worked through a step at a time.
(9¹)³
(9¹)³
(9) × (9) × (9)
(9¹)³=9³
n=3
- (9¹)³ means 3 copies of 9¹, all multiplied together.
- Each copy is 1 9, and there are 3 copies — so that is 1 × 3 = 3 of them.
- 3 9s multiplied together is 9³. So n = 3. The shortcut: a power raised to a power MULTIPLIES the exponents.