Numbers & Operations
Exponents (Including Fractional)
Exponents tell you how many times to multiply a base by itself. Fractional exponents connect to roots: x12 = √x, x13 = ∛x. The numerator is the power, the denominator is the root.
Watch & Learn
Watch a clear, friendly video explanation of Exponents (Including Fractional):
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Evaluate: 2⁵
Step-by-Step Solution
2⁵ means multiply 2 by itself 5 times.
2 × 2 = 4, × 2 = 8, × 2 = 16, × 2 = 32.
Answer
32
Problem
Evaluate: 2713
Step-by-Step Solution
A fractional exponent 13 means cube root.
2713 = ∛27
What number times itself 3 times equals 27? 3 × 3 × 3 = 27.
Answer
3
Problem
Evaluate: 1634
Step-by-Step Solution
Break it up: 1634 = (1614)³
1614 = ⁴√16 = 2 (since 2⁴ = 16)
2³ = 8
Answer
8
Problem
Evaluate: 5⁻²
Step-by-Step Solution
A negative exponent means take the reciprocal.
5⁻² = 1/5² = 1/25
Answer
1/25
Problem
Evaluate: (−3)⁴
Step-by-Step Solution
(−3)⁴ means multiply −3 by itself 4 times.
(−3) × (−3) = 9, then 9 × (−3) = −27, then −27 × (−3) = 81.
Even exponent → positive result.
Answer
81
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
Evaluate: 3⁴
Evaluate: 6412
Evaluate: 823
Evaluate: 5⁰
Evaluate: 432
Evaluate: 2⁶
Evaluate: 2723
Evaluate: 3⁻²
Evaluate: 10012
Evaluate: (−2)³
Evaluate: 12513
Evaluate: 2⁻³
Finished all 12? Give yourself a pat on the back — then check your work!
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