🧮 Math Calculator

Exponent Calculator

Calculate powers, roots, and fractional exponents with step-by-step solutions. Perfect for students, teachers, and anyone working with exponential mathematics.

Exponent Calculator

Calculate powers, roots, and fractional exponents with step-by-step solutions

Enter Values

Operation:
Power (base^exponent)
a^n

Exponent Rules

Power Rule: a^m × a^n = a^(m+n)

Quotient Rule: a^m ÷ a^n = a^(m-n)

Power of Power: (a^m)^n = a^(m×n)

Negative Power: a^(-n) = 1/(a^n)

Exponent Rules & Properties

a^m × a^n = a^(m+n)
a^m ÷ a^n = a^(m-n)
(a^m)^n = a^(m×n)
a^(-n) = 1/(a^n)
a^(1/n) = nth root of a
a^0 = 1 (for any a ≠ 0)

Understanding Exponents

Exponents represent repeated multiplication. When we write aⁿ, it means multiplying the base 'a' by itself 'n' times. This fundamental concept appears throughout mathematics and has numerous applications in science, engineering, and finance.

Our calculator supports various types of exponential operations:

  • Powers: Calculate aⁿ where n is a positive integer
  • Roots: Calculate the nth root of a number
  • Fractional Exponents: Handle decimal and fractional powers
  • Negative Exponents: Calculate reciprocals using negative powers

Understanding exponents is crucial for algebra, calculus, and many real-world applications like compound interest, population growth, and scientific notation.

How to Use This Calculator

1Select the type of exponential operation you want to perform
2Enter the base number and exponent (or root degree)
3Click "Calculate" to see the result and solution steps
4Review additional calculations and exponent rules

Real-World Applications

💰

Compound Interest

A = P(1 + r/n)^(nt) where P is principal, r is rate, n is compounding frequency, and t is time.

📊

Population Growth

P(t) = P₀e^(rt) where P₀ is initial population, r is growth rate, and t is time.

🔬

Scientific Notation

Large numbers like 6.022 × 10²³ (Avogadro's number) use powers of 10 for compact representation.