Exponent Calculator
Calculate powers, simplify exponent expressions, convert roots, and learn exponent rules with step-by-step visual explanations.
Background
Exponents show repeated multiplication, growth, roots, and scientific notation. This calculator helps students evaluate numeric powers and understand rules like product of powers, quotient of powers, power of a power, zero exponents, negative exponents, and fractional exponents.
How to use this calculator
- Choose Basic power, Negative exponents, Exponent rules, Roots & fractional exponents, or Scientific notation.
- Enter the base, exponent, variable, or scientific-notation values.
- Click Calculate Exponent.
- Review the answer, rule badges, visual model, and step-by-step explanation.
How this calculator works
- For numeric powers, it evaluates a^b and explains whether the exponent means repeated multiplication, reciprocal, root, or growth.
- For symbolic simplification, it applies standard exponent rules and keeps variables symbolic.
- For fractional exponents, it rewrites a^(m/n) as a radical expression.
- For scientific notation, it converts between decimal form and A × 10^n.
Formula & Rules Used
Product rule: a^m · a^n = a^(m+n)
Quotient rule: a^m / a^n = a^(m−n)
Power rule: (a^m)^n = a^(mn)
Negative exponent: a^−n = 1/a^n
Zero exponent: a^0 = 1, for a ≠ 0
Fractional exponent: a^(m/n) = (ⁿ√a)^m
Example Problems & Step-by-Step Solutions
Example 1: Basic exponent
Given: 2^5
Step: Write the exponent as repeated multiplication: 2 × 2 × 2 × 2 × 2.
Answer: 2^5 = 32.
Example 2: Negative exponent
Given: 5^−2
Step: Move the power to the denominator: 5^−2 = 1 / 5^2.
Answer: 1 / 25 = 0.04.
Example 3: Fractional exponent
Given: 27^(2/3)
Step: Rewrite as a cube root: (∛27)^2.
Answer: 3^2 = 9.
Frequently Asked Questions
What is an exponent?
An exponent tells how many times a base is used as a factor. For example, 2^5 means 2 × 2 × 2 × 2 × 2.
What does a negative exponent mean?
A negative exponent means reciprocal. For example, x^-3 = 1/x^3, as long as x is not 0.
What does a fractional exponent mean?
A fractional exponent represents a root. For example, x^(1/2) means the square root of x, and x^(1/3) means the cube root of x.
Why does a^0 equal 1?
For any nonzero base, the quotient rule gives a^m / a^m = a^(m−m) = a^0, and the same fraction also equals 1.
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