What is 2 to the 10th power?
2^10 = 1,024.
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Evaluate a^b for integer, negative, and fractional exponents—compound growth, scientific notation, and power laws in one local tool.
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a^b multiplies a by itself b times when b is a positive integer: 2^5 = 2×2×2×2×2 = 32. Negative exponents take reciprocals; fractional exponents express roots.
Outputs follow standard arithmetic exponent rules; verify financial, scientific, or compliance-critical calculations using your official method requirements.
Exponentiation is repeated multiplication in compact notation. Scientists write 6.02×10^23 instead of a 24-digit number; financiers model compound growth as principal × (1 + rate)^years.
**Integer exponents:** 3^4 = 3×3×3×3 = 81. **Negative exponents:** a^(−n) = 1/a^n. Example: 2^(−3) = 1/8 = 0.125.
**Fractional exponents:** a^(1/2) is the square root of a; a^(2/3) is the cube root of a². So 8^(2/3) = (∛8)² = 2² = 4.
**Power laws** chain exponents: (a^m)^n = a^(mn); a^m × a^n = a^(m+n). These rules underpin scientific notation, logarithms (inverse exponentials), and compound interest.
0^0 is undefined in this calculator. 0 to a negative power is undefined because it implies division by zero.
Enter base a and exponent b for a^b—handles negatives, fractions, and scientific-scale results locally.
Concise answers for common searches — definitions, steps, and comparisons.
2^10 = 1,024.
a^(−n) = 1/a^n. Example: 5^(−2) = 1/25 = 0.04.
a^(1/2) = √a. a^(2/3) means cube root of a, then square the result.
a^0 = 1 for any a ≠ 0. Zero to the zero power is undefined here.
Applies standard real exponent rules via JavaScript Math.pow with domain checks for 0^negative and invalid roots of negatives.
Formula
a^m × a^n = a^(m+n). (a^m)^n = a^(mn). a^(−n) = 1/a^n. a^(1/n) = ⁿ√a. Compound: A = P(1+r)^t.Positive, negative, or fractional base—e.g. 2, −3, or 0.25.
Integers, negatives, or fractions like 0.5 for square root.
0^(−2) and similar invalid forms show clear errors.
When b = 0.5, compare with dedicated √ tool for perfect squares.
Input
2^10Output
1,024Classic computing anchor—2^10 bytes in kilobyte discussions.
Input
10^(−3)Output
0.001Mill prefix in metric: one-thousandth.
Input
81^0.5Output
981^(1/2) = √81 = 9.
Input
1000 × 1.05^8Output
≈ 1,477.46Eight years at 5% annual growth on $1,000.
Input
(2^3)^4 = 2^12Output
4,096Multiply exponents: 3×4 = 12.
Input
(−2)^4Output
16Even powers remove sign; (−2)^3 would be −8.
$5,000 at 6% for 12 years: 5000 × 1.06^12 ≈ $10,045 without a spreadsheet.
Evaluate 3.2×10^7 as 3.2 × 10^7 = 32,000,000 for lab report checks.
2^20 = 1,048,576 bytes ≈ 1 MiB—verify powers of two in CS exercises.
Remaining fraction after t half-lives: (1/2)^t. After 3 half-lives: 0.125 of original.
Step-by-step chains that connect related tools for common tasks.
| Exponent | Value | Typical use |
|---|---|---|
| 2^8 | 256 | Byte address space |
| 2^10 | 1,024 | Kibibyte scale |
| 2^16 | 65,536 | 16-bit limit |
| 2^20 | 1,048,576 | Mebibyte |
| Expression | Exponent form | Decimal (approx) |
|---|---|---|
| √16 | 16^0.5 | 4 |
| ∛27 | 27^(1/3) | 3 |
| 16^(3/4) | fourth root of 16³ | 8 |
ⁿ√x = x^(1/n)—unifies root and power entry in one field.
If 2^x = 50, x = log(50)/log(2)—inverse problem for logarithm calculator.
10^3 meters is a kilometer scale—exponent applies to numeric part only.
(1/2)^t stays positive for integer t—decay fractions.
2^5 = 32, not 10. Exponent counts repeated multiplication, not multiplication of a and b.
2^3 × 2^2 = 2^5, not 2^5 + 2^3. Add exponents when bases match.
This tool treats 0^0 as undefined—some fields define it differently.
(-9)^0.5 has no real square root—result is not a real number.
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One million—six tens multiplied: 10×10×10×10×10×10 = 1,000,000.
Squaring multiplies two negatives: (−3)×(−3) = 9.
Yes—0.5 for square root, 0.333… approximates cube root (exact 1/3 is better).
A = P(1 + r)^t where t is periods. Each period multiplies by (1+r).
Logarithm. If a^x = y, then x = log_a(y)—use logarithm calculator.
Generally no. 2^3 = 8 but 3^2 = 9—order matters.
10^(−3) meters = 1 mm. Negative exponent = reciprocal with positive power.
Base and exponent values process locally in the browser.
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Reviewed by EverydayTools Editorial Team on 2026-07-03.
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Quick examples
Expression
2¹⁰
Result
1024
1024
Step 1 – Repeated multiplication
2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
Step 2 – Final result
2¹⁰ = 1024
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