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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 $$x^2$$ .
Explanation 2: Rewrite the denominator as negative exponent and then simplify.

### 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.