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
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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
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
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.