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Exponent Calculator

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How to Use This Calculator

Step 1: Enter the base — the number being multiplied by itself.

Step 2: Enter the exponent — how many times the base is multiplied. Can be negative or a decimal.

Step 3: Click Calculate to see the result, scientific notation, and step-by-step expansion.

What Are Exponents?

An exponent tells you how many times to multiply a number by itself. For example, 2 to the 3rd power (written 2³) means 2 × 2 × 2 = 8. The number being multiplied is the 'base', and the small raised number is the 'exponent' or 'power'.

Exponents are a shorthand for repeated multiplication, just as multiplication is shorthand for repeated addition.

Special cases: any non-zero number to the 0 power equals 1. A negative exponent means 'one divided by the positive version' — for example, 2⁻³ = 1/2³ = 1/8. A fractional exponent means a root: 9^(1/2) = √9 = 3.

Exponent Rules

aᵐ × aⁿ = aᵐ⁺ⁿ (multiplying same base: add exponents)
aᵐ ÷ aⁿ = aᵐ⁻ⁿ (dividing same base: subtract exponents)
(aᵐ)ⁿ = aᵐⁿ (power of a power: multiply exponents)
a⁰ = 1 (zero exponent, a ≠ 0)
a⁻ⁿ = 1/aⁿ (negative exponent)
a^(1/n) = ⁿ√a (fractional exponent = root)

Example: 2¹⁰
= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1,024

Common Exponents

ExpressionExpandedValue
2³2 × 2 × 28
5²5 × 525
10⁶10 × 10 × 10 × 10 × 10 × 101,000,000
3⁻²1 ÷ (3 × 3)0.1111
16^(1/2)√164
2¹⁰2 × 2 × ... (ten times)1,024

Examples

Example 1: 2¹⁰ = 1,024 — the reason 1 KB is roughly 1,000 bytes (technically 1,024).

Example 2: 10⁶ = 1,000,000 — how scientific notation expresses a million.

Example 3: 3⁻² = 0.1111... = 1/9 — negative exponent flips to the reciprocal.

Tips

0⁰ is indeterminate — most calculators return 1 by convention, but mathematicians disagree.

Negative base with fractional exponent can give complex results.

Scientific notation uses powers of 10 for very large or small numbers.

Compound interest relies on exponents — (1 + r)ⁿ grows rapidly.

Frequently Asked Questions

What does 0 raised to the 0 power equal?
This is one of the famous indeterminate forms in mathematics, and the answer depends on context. Most calculators — including JavaScript's built-in math — return 1, because the algebraic convention a to the zero equals 1 extends there. In calculus, however, the limit of 0 to the 0 depends on how you approach it and does not have a single value. For practical purposes, most calculators and computer algebra systems treat 0^0 as 1.
Why does any number to the 0 power equal 1?
This follows from the rule a to the m divided by a to the n equals a to the (m minus n). If you set m equal to n, you get a to the m divided by a to the m, which is obviously 1, and the rule gives a to the zero. Both must equal each other, so a to the zero must equal 1 for any non-zero base. This is a definition that makes all the other exponent rules work consistently.
How do negative exponents work?
A negative exponent means you divide by the positive version. So 2 to the negative 3 equals 1 divided by 2 to the 3, which is 1 over 8, or 0.125. The rule is a to the negative n equals 1 over a to the n. This makes the exponent rules extend naturally: dividing by a to the 3 gives the same result as multiplying by a to the negative 3.
What does a fractional exponent mean?
A fractional exponent represents a root. Specifically, a to the power of 1 over n equals the nth root of a. So 9 to the 1/2 equals the square root of 9, which is 3. Similarly, 8 to the 1/3 equals the cube root of 8, which is 2. More generally, a to the m over n equals the nth root of a to the m — or equivalently, (the nth root of a) to the m.
Why do very large exponents produce such enormous numbers?
Exponential growth multiplies the current value by the base with every increase. Each additional power of 2 doubles the result: 2, 4, 8, 16, 32, 64, 128, 256, 512, 1,024. This is why compound interest, population growth, and viral content can produce surprisingly large values over time — the growth rate compounds on itself. After 30 years at 7 percent annual growth, an investment is about 7.6 times its original size, not roughly 3 times as simple interest would suggest.
What is the difference between 2 to the 10th and 10 to the 2nd?
They are very different. 2 to the 10th means 2 multiplied by itself 10 times, which equals 1,024. 10 to the 2nd means 10 multiplied by itself twice, which equals 100. Exponents are not commutative — the base and exponent play different roles. The only exceptions are special coincidences like 2 to the 4 equals 4 to the 2, both equal 16, where the values happen to match.

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