2 to the 10th power
- Base (b)
- 2
- Exponent (n)
- 10
Result b raised to the power n: 1024
Scientific notation: 1.024 × 10^3
Reciprocal (b^-n): 0.0009765625
- 2^10 = 1024
Ten factors of 2 multiply out to 1024, the number of bytes in a kibibyte.
Exponent Calculator
An exponent says how many times a base is multiplied by itself: b^n means n factors of b. For example, 2^10 = 2 × 2 × … × 2 = 1024. A negative exponent gives the reciprocal (10^-3 = 0.001), and a fractional one gives a root (2^0.5 ≈ 1.41421).
About this tool
Students checking homework, programmers sizing memory in powers of two and anyone converting between SI prefixes run into powers constantly. Enter a base and an exponent and the result appears in plain decimal form, with the same value in scientific notation and its reciprocal beside it. For small whole exponents the working is written out as a chain of multiplications; negative exponents are shown as one divided by the positive power, and fractional exponents through the natural logarithm. Very large or very small answers switch to a mantissa times a power of ten so the digits stay readable. One limit: results are real numbers only, so a negative base with a fractional exponent such as (-8)^0.5 is rejected rather than returned as a complex number, and values beyond about 1.8 × 10^308 cannot be represented.
How to use it
Enter the base
Type the number being multiplied, such as 2, 10, 1.05 or -3.
Enter the exponent
Use a whole number for repeated multiplication, a negative number for a reciprocal, or a decimal such as 0.5 for a root.
Read the result and working
The power appears with its scientific notation, its reciprocal and the steps used to reach it.
Examples
10 to the power -3
- Base (b)
- 10
- Exponent (n)
- -3
Result b raised to the power n: 0.001
Scientific notation: 1 × 10^-3
Reciprocal (b^-n): 1000
- 10^-3 = 1 ÷ 10^3
- = 1 ÷ 1000 = 0.001
A negative exponent flips the power into a fraction: 1 ÷ 10³ = 0.001, the SI milli factor.
2 to the power 0.5
- Base (b)
- 2
- Exponent (n)
- 0.5
Result b raised to the power n: 1.41421356237
Scientific notation: 1.414214 × 10^0
Reciprocal (b^-n): 0.707106781187
- 2^0.5 = e^(0.5 × ln 2) = e^0.346574
- = 1.41421356237
An exponent of one half is a square root, so the result is √2, about 1.41421356237.
How it is calculated
b^n = b × b × … × b (n factors); b^-n = 1 ÷ b^n; b^(p/q) = q-th root of b^p
b- the base
n- the exponent or power
For a positive whole exponent the base is multiplied by itself n times. Any non-zero base raised to 0 equals 1, and a negative exponent is the reciprocal of the matching positive power. For a fractional exponent the calculation uses b^n = e^(n × ln b), which equals a root: an exponent of 0.5 is the square root and 1/3 is the cube root. Results are computed in double-precision floating point and shown to 12 significant digits.
When not to use it
- Exact integer results beyond about 16 digits, such as 3^50, need arbitrary-precision software.
- Complex results from a negative base and a fractional exponent are outside its scope.
- Solving for an unknown exponent calls for a logarithm, not a power.
Common mistakes
- Treating -3^2 as (-3)^2: written without brackets it means -(3^2) = -9, while this tool squares the base -3 to get 9.
- Reading a negative exponent as a negative result; 2^-3 is 0.125, not -8.
- Multiplying base by exponent, so 5^3 becomes 15 instead of 125.
Frequently asked questions
Why does any number to the power zero equal 1?
Each step down in the exponent divides by the base once: 2^3 = 8, 2^2 = 4, 2^1 = 2, so 2^0 = 2 ÷ 2 = 1. The same pattern holds for every non-zero base. Zero to the power zero is treated here as 1, the convention used in algebra and combinatorics, though calculus treats it as indeterminate.
What does a negative exponent mean?
It means the reciprocal of the positive power. 10^-3 is 1 ÷ 10^3 = 0.001, and 2^-4 is 1 ÷ 16 = 0.0625. The sign of the result does not change; only its size shrinks below 1 for bases greater than 1.
How is a fractional exponent related to roots?
An exponent of 1/q takes the q-th root, so 9^0.5 = 3 and 27^(1/3) = 3. An exponent p/q takes the q-th root and then raises it to p, so 8^(2/3) = 2^2 = 4. Enter the fraction as a decimal, keeping in mind that 1/3 typed as 0.333333 gives a slightly rounded answer.
Why is a negative base with a decimal exponent rejected?
A value like (-8)^0.5 is the square root of -8, which is not a real number. Its true value is the imaginary number 2.828i. Since only real results are returned, the exponent field shows an error instead of a misleading figure.
How large a power can be computed?
Double-precision numbers top out near 1.8 × 10^308, so 10^308 works but 10^309 overflows and is reported as an error. At the small end, results under about 5 × 10^-324 underflow to 0 and are reported as an error.
Why is 3^40 not shown with every digit?
Floating-point arithmetic keeps about 15 to 17 significant digits. 3^40 is 12,157,665,459,056,928,801, which has 20 digits, so the last few cannot be held exactly and the result is shown in scientific notation instead.
Cite this tool
Using this tool in an assignment, article or report? Copy a citation, or a link for your website.
APA
Tools Directory Editorial Team. (2026, October 25). Exponent Calculator. Tools Directory. Retrieved October 26, 2026, from https://tools.milunir.com/math/algebra-tools/exponent-calculator/
MLA
Tools Directory Editorial Team. “Exponent Calculator.” Tools Directory, 25 Oct. 2026, https://tools.milunir.com/math/algebra-tools/exponent-calculator/. Accessed 26 Oct. 2026.
Chicago
Tools Directory Editorial Team. “Exponent Calculator.” Tools Directory. Last modified October 25, 2026. Accessed October 26, 2026. https://tools.milunir.com/math/algebra-tools/exponent-calculator/.
Link
<a href="https://tools.milunir.com/math/algebra-tools/exponent-calculator/">Exponent Calculator – Tools Directory</a>