Exponent Calculator

1. Enter the base, the number being raised to a power.
2. Enter the exponent. It can be negative, fractional or zero.
3. Read the result of the base raised to that power.
4. See the reciprocal and the scientific notation form.

Here is what each result means:

An exponent tells you how many times to multiply a number, the base, by itself. In b^n, b is the base and n is the exponent, so 2^3 = 2 x 2 x 2 = 8. Exponents are a compact way to write repeated multiplication, just as multiplication is repeated addition.

The idea extends beyond whole numbers. A negative exponent means a reciprocal, so b^-n = 1 / b^n. A fractional exponent means a root, so b^(1/2) = sqrt(b). And any nonzero base to the power zero equals one.

It raises the base to the exponent using the power operation, then also shows the reciprocal and scientific-notation forms.

1. For a whole exponent, multiply the base by itself that many times.
2. For a negative exponent, take the reciprocal of the positive-power result.
3. For a fractional exponent, take the matching root of the base.

When the exponent is one half, the result is a square root, which the square root calculator gives directly.

Take 2^10 and 10^-3.

Calculation: 2^10 = 1024, found by multiplying 2 by itself ten times. And 10^-3 = 1 / 10^3 = 0.001, a reciprocal. A fractional case, 64^(1/2) = sqrt(64) = 8, shows an exponent acting as a root.

The exponent changes what the operation means.

One rule covers them all: a base raised to a power, with negatives flipping to reciprocals and fractions becoming roots.

Exponents connect to multiplication and roots as inverse and shorthand ideas.

Seeing these links makes the exponent rules feel natural rather than a list to memorize.

The Size of the Base

A larger base grows far faster as the exponent rises, since each step multiplies by more.

The Sign of the Exponent

A positive exponent grows the number; a negative one shrinks it toward zero as a reciprocal.

Whole vs Fractional Exponent

A whole exponent multiplies; a fractional one takes a root, which can make the result smaller than the base.

Homework and Algebra

Evaluate powers quickly, including negative and fractional exponents.

Science and Growth

Work out powers of ten for scientific notation, or growth over repeated periods.

Computing and Data

Find powers of two for memory sizes, where 2 to the 10th is a kilobyte scale.

1. Multiplying Base by Exponent

2 to the 3rd is 8, not 6. The exponent counts multiplications, it is not a factor.

2. Mishandling a Negative Exponent

A negative exponent gives a reciprocal, not a negative number. 2 to the -2 is 0.25, not -4.

3. Zero to the Zero

Any nonzero base to the power zero is one, but zero to the zero is a special, debated case.

4. Negative Base with a Fraction

A negative base to a fractional power has no real value. Expect undefined here.

5. Order of Operations

Exponents come before multiplication and addition. Apply the power first.

The power rule is exact; only display decimals and very large results are rounded.

An exponent tells you how many times to multiply a base by itself. In 2 to the 3rd, the exponent 3 means 2 times 2 times 2, which is 8. It is shorthand for repeated multiplication.

Multiply the base by itself as many times as the exponent says. For 5 to the 4th, that is 5 times 5 times 5 times 5, which is 625. This tool does it for any base and exponent.

A negative exponent means the reciprocal of the positive power. So 2 to the -3 is 1 divided by 2 to the 3rd, which is 1 over 8, or 0.125. It is not a negative number.

A fractional exponent is a root. A power of one half is a square root, and one third is a cube root. So 64 to the one half is the square root of 64, which is 8.

Any nonzero number to the power of zero equals one. This keeps the exponent rules consistent. Zero to the power of zero is a special, debated case.

Taking an even root of a negative number has no real value. So a negative base with a fractional exponent gives an undefined result here, since the tool works with real numbers.

Scientific notation writes a number as a value times a power of ten. Powers of ten are exponents, so 3,000 is 3 times 10 to the 3rd. The tool shows this form for large or small results.

A root is the inverse of an exponent. Raising to a power multiplies the base repeatedly, while a root asks which number, raised to that power, gives the value. A fractional exponent is a root.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Exponentiation (Wikipedia).
• Exponents explained (Maths Is Fun).
• Negative and fractional exponents (Maths Is Fun).