Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.
-$\frac{7 \mathrm{r}^{-2}\left(\mathrm{r}^{4}\right)^{4}}{13\left(\mathrm{r}^{-1}\right)^{5}}$

A) $\frac{7}{13 r^{2}}$

B) $\frac{7 \mathrm{r}^{19}}{13}$

C) $\frac{7 \mathrm{r}^{2}}{13}$

D) $\frac{7}{13 r^{19}}$

Question

Simplify the expression so that no negative exponents appear in the final result. Assume all variables represent nonzero numbers.
-$\frac{7 \mathrm{r}^{-2}\left(\mathrm{r}^{4}\right)^{4}}{13\left(\mathrm{r}^{-1}\right)^{5}}$

A) $\frac{7}{13 r^{2}}$

B) $\frac{7 \mathrm{r}^{19}}{13}$

C) $\frac{7 \mathrm{r}^{2}}{13}$

D) $\frac{7}{13 r^{19}}$

Quizplus · Accepted Answer

The expression simplifies to $\frac{7 \mathrm{r}^{19}}{13}$ by applying the laws of exponents: $\mathrm{r}^{-2} \cdot (\mathrm{r}^{4})^{4} = \mathrm{r}^{-2} \cdot \mathrm{r}^{16} = \mathrm{r}^{14}$ and $(\mathrm{r}^{-1})^{5} = \mathrm{r}^{-5}$. Thus, $\frac{\mathrm{r}^{14}}{\mathrm{r}^{-5}} = \mathrm{r}^{19}$.

Simplify the Expression So That No Negative Exponents Appear in the Final