The Quotient Rule

Watch one or both videos to understand the Quotient Rule for exponents.

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

When you are dividing two exponential expressions that have the same base, you write the base once. The new exponent will be the exponent in the denominator subtracted from the exponent in the numerator.

Complete this statement of the Quotient Rule:
$\displaystyle \frac{{v}^{{k}}}{{v}^{{h}}}$ = Preview Question 6 Part 1 of 4  

Simplify the expression completely.
$\displaystyle \frac{{y}^{{19}}}{{y}^{{8}}}$ = Preview Question 6 Part 2 of 4  

Simplify this expression.
$\displaystyle \frac{{3}^{{6}}}{{3}^{{2}}}$ = Preview Question 6 Part 3 of 4  

Compare the previous examples to the one below. Remember that exponents happen before subtraction in the order of exponents.
Simplify. $\displaystyle {2}^{{7}}-{2}^{{4}}$ = Preview Question 6 Part 4 of 4