Exponent Calculator
Calculate Exponents with Ease
Enter values into any two of the input fields to solve for the third. Understand the mathematics behind exponents with detailed explanations.
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Exponent Calculator
Steps:
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Understanding Exponents
What is an exponent?
Exponentiation is a mathematical operation, written as \(a^n\), involving the base \(a\) and an exponent \(n\). In the case where \(n\) is a positive integer, exponentiation corresponds to repeated multiplication of the base, \(a\) times.
The calculator above accepts negative bases, but does not compute imaginary numbers. It also does not accept fractions directly, but can be used to compute fractional exponents, as long as the exponents are input in their decimal form.
Basic exponent laws and rules
Multiplying exponents with same base:
\(a^n \times a^m = a^{n+m}\)
Example: \(2^3 \times 2^4 = 2^{3+4} = 2^7 = 128\)
Negative exponents:
\(a^{-n} = \frac{1}{a^n}\)
Example: \(2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125\)
Dividing exponents with same base:
\(\frac{a^n}{a^m} = a^{n-m}\)
Example: \(\frac{2^5}{2^3} = 2^{5-3} = 2^2 = 4\)
Power of a power:
\((a^m)^n = a^{m \times n}\)
Example: \((2^3)^2 = 2^{3 \times 2} = 2^6 = 64\)
Power of a product:
\((a \times b)^n = a^n \times b^n\)
Example: \((2 \times 3)^2 = 2^2 \times 3^2 = 4 \times 9 = 36\)
Power of a quotient:
\(\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}\)
Example: \(\left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2} = \frac{4}{9} \approx 0.444\)
Zero exponent:
\(a^0 = 1\) (for any a ≠ 0)
Example: \(5^0 = 1, (-3)^0 = 1\)
Fractional exponents:
\(a^{\frac{1}{n}} = \sqrt[n]{a}\)
Example: \(8^{\frac{1}{3}} = \sqrt[3]{8} = 2\)
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