Exponent Calculator

How to use the exponent calculator

Enter a base and an exponent (also called a power or index) and the calculator returns bⁿ. It handles every kind of exponent:

• Whole numbers — 2¹⁰ = 1,024
• Zero — any non-zero number to the power 0 is 1
• Negative exponents — 2⁻³ = 1/8 = 0.125
• Fractional and decimal exponents — 8^2/3 = 4; enter 2/3 as 0.666666666667
• Enormous results — 2⁵⁰⁰⁰ is shown in scientific notation together with its number of digits

The steps explain what the exponent means, and a table lists the powers of your base from −3 to 12.

Exponent rules

All of these follow from the basic idea that a whole-number exponent counts how many times the base is multiplied by itself. For instance b⁰ = 1 because b³ ÷ b³ must be 1, and the rule b^m ÷ bⁿ = b^m−n turns that into b⁰.

Worked examples

2 to the power of 10

2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024. That is why a kilobyte was historically 1,024 bytes — it is the power of 2 closest to 1,000.

A negative exponent

5⁻² = 1 ÷ 5² = 1 ÷ 25 = 0.04. A negative exponent never makes the answer negative; it makes it a reciprocal.

A fractional exponent

27^2/3 means "the cube root of 27, squared": ∛27 = 3, and 3² = 9. The denominator of the fraction is the root and the numerator is the power. A power of ½ is simply a square root — see the square root calculator for simplified radical forms.

Negative bases

A negative base raised to an even whole power is positive and to an odd power is negative: (−3)² = 9 but (−3)³ = −27. Watch the brackets: −3² written without them usually means −(3²) = −9.

With a fractional exponent, a negative base only gives a real answer when the root is odd. (−8)^1/3 = −2 because (−2)³ = −8, but (−4)^1/2 has no real value — it is the imaginary number 2i. The calculator detects simple fractions with denominators up to 12 and tells you when the result is not real.

Where exponents are used

• Compound growth: money growing at 7% a year for 10 years becomes 1.07¹⁰ ≈ 1.967 times larger. Explore this with the compound interest calculator.
• Science: very large and small quantities are written with powers of 10, e.g. 6.022 × 10²³. See the scientific notation calculator.
• Computing: memory and address sizes are powers of 2 — 2³² ≈ 4.3 billion.
• Area and volume: squaring and cubing lengths, as in A = πr².

The inverse of exponentiation is the logarithm: if bⁿ = x then n = log_b(x). Use the logarithm calculator to find an unknown exponent.