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Subtract Exponents of like bases

Formula and examples of how to subtract exponents

Formula and Examples

$ \frac{ x^m} {x^n} = x^{m \red - n} $

Example

$ \frac{ x^5} {x^3} = x^{5 \red - 3} = x ^2 $

Why this works

There are two ways to demonstrate the reason behind this formula

Explanation 1: If you expand the numerator and the denominator, you can see that we cancel several x's that are common factors. All that remains is $$ x \cdot x $$ which, of course, is $$ x^2 $$ . Example 1 - Factored explanation
Explanation 2: Rewrite the denominator as negative exponent and then simplify. Example 1 - Negative explanation

Substract Exponents Solver

Enter any exponential equation into the algebra solver below :

Practice Problems

Use the formula for subtracting exponents to simplify each expression below.

Problem 1
Practice Problem 1
Problem 2
Practice Problem 2
Problem 3
Practice Problem 3
Problem 4
Practice Problem 4

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