Exponent Calculator
Calculate any base raised to any power with step-by-step solutions
Calculate Exponents
The number being multiplied by itself
The power to which the base is raised
Result
Step-by-Step Solution
Laws of Exponents
Product Rule
xm × xn = xm+n
Quotient Rule
xm ÷ xn = xm-n
Power Rule
(xm)n = xmn
Zero Rule
x0 = 1 (x ≠ 0)
Negative Rule
x-n = 1/xn
Special Cases
Fractional Exponents
x1/n = ⁿ√x (nth root)
Negative Exponents
Move to denominator and make positive
Zero Exponent
Any base to power 0 equals 1
Large Numbers
Use scientific notation for clarity
Understanding Exponents
What is an Exponent?
An exponent represents how many times a number (the base) is multiplied by itself. For example, 2³ means 2 × 2 × 2 = 8. The small number (3) is the exponent, and the larger number (2) is the base.
How to Calculate by Hand
- 1.Identify the base and exponent (e.g., 3⁵)
- 2.Write the base multiple times (3 × 3 × 3 × 3 × 3)
- 3.Multiply from left to right
- 4.Get the final result (243)
Types of Exponents
Positive Integer
2⁴ = 2 × 2 × 2 × 2 = 16
Standard multiplication repeated
Zero Exponent
5⁰ = 1
Any base to power 0 equals 1
Negative Exponent
3⁻² = 1/3² = 1/9
Reciprocal of positive exponent
Fractional Exponent
8^(1/3) = ³√8 = 2
Related to roots
Real-World Applications
Population Growth
Bacteria double every 20 minutes. After 3 hours (9 periods): 2⁹ = 512 bacteria
Compound Interest
$1000 at 5% annually for 10 years: 1000 × (1.05)¹⁰ = $1,628.89
Computer Science
Binary system uses powers of 2. 8-bit number: 2⁸ = 256 possible values