Power / Exponent Calculator

Calculate exponents, roots, and powers with detailed explanations

Calculate baseexponent = result

Common Powers and Roots

Squares (n²)

= 1
= 4
= 9
= 16
= 25

Cubes (n³)

= 1
= 8
= 27
= 64
= 125

Square Roots (√n)

√1= 1
√4= 2
√9= 3
√16= 4
√25= 5

Cube Roots (∛n)

∛1= 1
∛8= 2
∛27= 3
∛64= 4
∛125= 5

Exponent Rules

aᵐ × aⁿ = aᵐ⁺ⁿ
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
(aᵐ)ⁿ = aᵐⁿ
a⁻ⁿ = 1/aⁿ
a⁰ = 1 (a ≠ 0)
a¹/ⁿ = ⁿ√a

Exponentiation is a mathematical operation involving two numbers: the base and the exponent.

Power / Exponent Calculator - Calculate Exponents, Roots & Powers

Our free power and exponent calculator helps you perform complex mathematical operations involving exponents, roots, and powers with detailed step-by-step explanations. Calculate exponential growth, roots of any degree, and scientific notation effortlessly.

Perfect for students learning algebra, scientific calculations, engineering computations, and financial modeling. Understand the mathematical principles behind exponents and powers through comprehensive explanations.

How to Use This Power & Exponent Calculator

Step 1: Enter Base and Exponent

  • Input the base number (the number being raised)
  • Enter the exponent or power (positive, negative, fractional)
  • Choose calculation type: power, root, or scientific notation

Step 2: Analyze Results

  • View detailed step-by-step calculation process
  • Learn the mathematical rules applied
  • Get multiple representations of results

Why Use Our Power & Exponent Calculator?

All Exponent Types

Handle positive exponents, negative exponents, fractional exponents (roots), zero exponents, and decimal exponents with precision and detailed explanations.

Root Calculations

Calculate square roots, cube roots, and roots of any degree using fractional exponents. Understand the relationship between roots and exponents.

Scientific Notation

Convert numbers to and from scientific notation, perform calculations with very large or very small numbers, and understand significant figures.

Educational Explanations

Learn exponent rules, properties, and applications through detailed step-by-step solutions that show the mathematical reasoning behind each calculation.

Comprehensive Math Learning Tool

Used by students, teachers, scientists, and engineers worldwide for accurate exponent calculations and mathematical education.

Frequently Asked Questions (FAQ)

What are the basic rules of exponents?

The fundamental exponent rules include: Product Rule (aᵐ × aⁿ = aᵐ⁺ⁿ), Quotient Rule (aᵐ ÷ aⁿ = aᵐ⁻ⁿ), Power Rule ((aᵐ)ⁿ = aᵐⁿ), Zero Exponent (a⁰ = 1), and Negative Exponent (a⁻ⁿ = 1/aⁿ).

How do fractional exponents work?

Fractional exponents represent roots. For example, a¹/² means the square root of a, a¹/³ means the cube root of a, and aᵐ/ⁿ means the nth root of a raised to the m power. Our calculator shows the step-by-step conversion between fractional exponents and radical form.

What's the difference between 2³ and 3²?

means 2 × 2 × 2 = 8 (2 raised to the 3rd power), while means 3 × 3 = 9 (3 raised to the 2nd power). The base and exponent positions matter significantly in the result. Our calculator explains this distinction clearly.

How do negative exponents work?

Negative exponents indicate reciprocals. For example, a⁻ⁿ = 1/aⁿ. So 2⁻³ = 1/2³ = 1/8 = 0.125. Negative exponents don't make the result negative; they create fractions. Our calculator demonstrates this conversion process step-by-step.

What is scientific notation and when is it used?

Scientific notation expresses numbers as a coefficient between 1 and 10 multiplied by 10 raised to a power. It's used for very large numbers (like 3.00 × 10⁸ m/s for light speed) or very small numbers (like 1.67 × 10⁻²⁷ kg for proton mass). Our calculator handles scientific notation conversions and calculations.