Math · Powers & Roots
Exponent
Calculator
Calculate bⁿ, find nth roots, or solve for an unknown base or exponent. Supports negative and fractional exponents with a full rules reference.
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bⁿ Result
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Scientific
Solve for Base, Exponent or Result
💡 Select what to solve for, fill the other two fields, then click Calculate.
bn
=
?
base
exp
result
Result
2¹⁰
1024
1.024 × 10³
Reciprocal
0.000977
√result
32
bⁿ
1024
b⁻ⁿ
0.000977
√result
32
ⁿ√b
1.0718
📋 Powers Reference Table
📐 Exponent Rules
Product Rule
bᵐ × bⁿ = bᵐ⁺ⁿ
2³ × 2⁴ = 2⁷ = 128
Quotient Rule
bᵐ ÷ bⁿ = bᵐ⁻ⁿ
2⁶ ÷ 2² = 2⁴ = 16
Power Rule
(bᵐ)ⁿ = bᵐⁿ
(2³)² = 2⁶ = 64
Zero Exponent
b⁰ = 1
Any non-zero base to 0 = 1
Negative Exponent
b⁻ⁿ = 1/bⁿ
2⁻³ = 1/8 = 0.125
Fractional Exponent
b^(1/n) = ⁿ√b
8^(1/3) = ∛8 = 2
Product to Power
(ab)ⁿ = aⁿbⁿ
(2×3)² = 4×9 = 36
Quotient to Power
(a/b)ⁿ = aⁿ/bⁿ
(2/3)² = 4/9
Understanding Exponents
An exponent tells you how many times to multiply a base by itself. Written as bⁿ — b is base, n is the exponent. Exponents are fundamental to algebra, scientific notation, calculus, and computing.
Key Formulas
Standard: bⁿ = b × b × b … (n times)
Negative: b⁻ⁿ = 1/bⁿ
Fractional: b^(m/n) = (ⁿ√b)ᵐ
Find exponent: n = log(result) / log(base)
Find base: b = ⁿ√result = result^(1/n)
What is 0⁰?
0⁰ is mathematically indeterminate but in most practical contexts (combinatorics, polynomials) it equals 1. This calculator returns 1 for 0⁰ following common convention.
Can the base be negative?
Yes with integer exponents: (−b)ⁿ is positive when n is even, negative when odd. With fractional exponents, negative bases produce complex numbers which this calculator cannot handle.
How do I find the exponent from base and result?
Use logarithms: n = log(result)/log(base). For 2ⁿ=32: n = log(32)/log(2) = 5. Use "Find Exp" mode above.