What should you do when dividing powers with the same base?

When dividing powers with the same base, the correct approach is to subtract the exponents. This follows from one of the fundamental properties of exponents, specifically the quotient rule.

According to the quotient rule, if you have a base ( a ) raised to the power of ( m ) divided by the same base ( a ) raised to the power of ( n ), it can be mathematically expressed as:

[

\frac{a^m}{a^n} = a^{m-n}

]

This means that when performing the division, you take the exponent of the numerator and subtract the exponent of the denominator, resulting in a new exponent that represents the power of the base ( a ) after division.

For example, if you have ( \frac{x^5}{x^2} ), you would subtract the exponents:

[

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

]

This property allows for simplification in calculations involving exponents, ensuring that when bases are the same, you can handle the operations efficiently by simply adjusting the exponents. Thus, using the subtraction of exponents is essential for solving problems involving division