Simplify the expression. Assume all variables represent nonnegative real numbers.
-$\sqrt[5]{r} \cdot \sqrt{r}$
A) $\sqrt[7]{r^{2}}$
B) $\sqrt[7]{2 r}$
C) $\sqrt[10]{\mathrm{r}^{7}}$
D) $\sqrt[5]{\mathrm{r}^{2}}$

Question

Quizplus · Accepted Answer

To simplify the expression $\sqrt[5]{r} \cdot \sqrt{r}$, we convert the square root to a fractional exponent: $\sqrt{r} = r^{1/2}$. Thus, the expression becomes $r^{1/5} \cdot r^{1/2}$. Adding the exponents (since the bases are the same and we're multiplying), we get $r^{1/5 + 2/5} = r^{3/5}$. However, to match the given options, we express $3/5$ as $6/10$, which gives $r^{6/10} = \sqrt[10]{r^6}$. This is not directly matching any of the options, indicating a mistake in my explanation. The correct approach is to recognize that multiplying roots with the same base can be combined by multiplying their exponents in fractional form, leading to $r^{1/5} \cdot r^{1/2} = r^{1/5 + 5/10} = r^{2/10 + 5/10} = r^{7/10} = \sqrt[10]{r^7}$, correctly matching option C.

Simplify the Expression r5⋅r\sqrt[5]{r} \cdot \sqrt{r}5r​⋅r​ A) r27\sqrt[7]{r^{2}}7r2​ B) 2r7\sqrt[7]{2 r}72r​ C) r710\sqrt[10]{\mathrm{r}^{7}}10r7​ D) r25\sqrt[5]{\mathrm{r}^{2}}5r2​

Simplify the Expression $\sqrt[5]{r} \cdot \sqrt{r}$ A) $\sqrt[7]{r^{2}}$ B) $\sqrt[7]{2 r}$ C) $\sqrt[10]{\mathrm{r}^{7}}$ D) $\sqrt[5]{\mathrm{r}^{2}}$