Exponent Calculator Online Free Tool
Exponent Calculator
Power Calculator
Example: 25 = 2 × 2 × 2 × 2 × 2 = 32
An exponent (or power) tells you how many times to multiply a base number by itself. This calculator handles any base and exponent including decimals, fractions, and negative values. It also supports roots (fractional exponents) and scientific notation output for very large or small results.
Exponent Rules
The exponent rules (laws of exponents) are the foundation of algebraic manipulation. Mastering these allows you to simplify complex expressions and solve equations involving powers.
Product rule: aᵐ × aⁿ = aᵐ⁺ⁿ Quotient rule: aᵐ / aⁿ = aᵐ⁻ⁿ Power of power: (aᵐ)ⁿ = aᵐⁿ Zero exponent: a⁰ = 1 (a ≠ 0) Negative exponent: a⁻ⁿ = 1/aⁿ Fractional exponent: a^(1/n) = ⁿ√a
Example: 2⁻³ = 1/2³ = 1/8. And 8^(1/3) = ³√8 = 2.
Scientific Notation
Scientific notation expresses very large or small numbers as a coefficient (1-10) times a power of 10. It is used in science to handle numbers like the speed of light (3 × 10⁸ m/s) or the mass of an electron (9.1 × 10⁻³¹ kg). The exponent tells you how many places to move the decimal point.
Large number: 4,500,000 = 4.5 × 10⁶ Small number: 0.00023 = 2.3 × 10⁻⁴ Multiply: (2 × 10³) × (3 × 10⁴) = 6 × 10⁷
Frequently Asked Questions
Why does anything to the power of 0 equal 1?⌄
Using the quotient rule: aᵐ / aᵐ = aᵐ⁻ᵐ = a⁰. But aᵐ / aᵐ is clearly 1 (any number divided by itself is 1). Therefore a⁰ = 1 for any non-zero a. The expression 0⁰ is indeterminate and evaluated by convention as 1 in many mathematical contexts.
What does a negative exponent mean?⌄
A negative exponent means the reciprocal of the positive exponent. 2⁻³ = 1/2³ = 1/8 = 0.125. Negative exponents do not make the result negative, they make it a fraction less than 1 (for bases greater than 1).
What is the difference between an exponent and a radical?⌄
A radical (root) is a fractional exponent. The square root is the same as the 1/2 power: √9 = 9^(1/2) = 3. The cube root is the 1/3 power: ³√27 = 27^(1/3) = 3. This connection allows radical expressions to be manipulated using the same exponent rules as integer powers.
How do you calculate a fractional exponent like 8^(2/3)?⌄
8^(2/3) = (8^(1/3))² = (³√8)² = 2² = 4. Or equivalently: 8^(2/3) = (8²)^(1/3) = 64^(1/3) = 4. You can take the root first (usually easier) or the power first, both give the same result.