Question

Which expression is equivalent to \frac{r^9}{r^3}

Answer 1

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$\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup$

r^6

$\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup$

To simplify this we need to use the division property of exponents:

$\large\boxed{\mathtt{\frac{x^m}{x^n} =x^{m-n}}}$. So if we divide two numbers with the same base, we subtract their exponents.

Let's apply this rule here.

$\twoheadrightarrow\sf r^9\div r^3$.

$\bullet$ Since these two numbers have the same base, we subtract their exponents

$\twoheadrightarrow\sf r^6$

$\bullet$ Great job! We found the answer

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Answer 2

Answer: $\frac{r^9}{r^3} = r^{9-3} = r^6$

We subtract the exponents when dividing terms with the same base.

The general rule is $\frac{a^b}{a^c} = a^{b-c}$