Answer
r
Work Step by Step
$\displaystyle \frac{7^{-1/3}\cdot 7r^{-3}}{7^{2/3}\cdot(r^{-2})^{2}}=$
... numerator: $a^{m}\cdot a^{n}=a^{m+n}$ ,
... denominator: $(a^{m})^{n}=a^{mn}$ ...
$=\displaystyle \frac{7^{-1/3+1}r^{-3}}{7^{2/3}r^{-4}}$ = ...... use: $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$
$=7^{-1/3+3/3-2/3}\cdot r^{-3-(-4)}$
$=7^{0}r^{-3+4}$
$=1\cdot r^{1}$
$=r$
