Dividing Exponents Calculator
Calculate the quotient of two exponential expressions with step-by-step solutions
Calculate Exponential Division
Expression:
Base of numerator
Exponent of numerator
Base of denominator
Exponent of denominator
Division Result
Step-by-Step Solution:
Rule Applied:
Quotient Rule for Same Base: x^a ÷ x^b = x^(a-b)
When dividing exponents with the same base, subtract the exponents.
Quick Examples
Exponent Division Rules
Same Base
x^a ÷ x^b = x^(a-b)
Subtract exponents
Zero Exponent
x^0 = 1
Any non-zero base to power 0
Negative Exponent
x^(-n) = 1/x^n
Reciprocal of positive exponent
Power of Powers
(x^a)^b = x^(a×b)
Multiply exponents
Division Strategies
Same bases: Use quotient rule (subtract exponents)
Different bases: Use prime factorization
Negative exponents: Apply reciprocal rule
Large numbers: Factor into primes first
Understanding Exponential Division
What is Exponential Division?
Exponential division involves dividing one exponential expression by another. The approach depends on whether the bases are the same or different. When bases are the same, we use the quotient rule. When bases are different, we often use prime factorization.
Key Rules
- •Quotient Rule: x^a ÷ x^b = x^(a-b)
- •Zero Exponent: x^0 = 1 (x ≠ 0)
- •Negative Exponent: x^(-n) = 1/x^n
When to Use Each Method
- •Same bases: Apply quotient rule directly
- •Different bases: Use prime factorization
- •Related bases: Express in terms of common base
- •Complex cases: Combine multiple strategies
Note: Division by zero is undefined, so the denominator base cannot be zero when the exponent makes the entire expression zero.