Ricky Arias

2022-11-22

Which of the following is the correct radical form of this expression
$\left(\frac{{p}^{12}{q}^{\frac{3}{2}}}{64}{\right)}^{\frac{5}{6}}$
$A\right)\left(\sqrt[6]{\frac{{p}^{12}{q}^{\frac{3}{2}}}{64}}{\right)}^{5}\phantom{\rule{0ex}{0ex}}B\right)\left(\sqrt[5]{\frac{{p}^{12}{q}^{\frac{3}{2}}}{64}}{\right)}^{6}\phantom{\rule{0ex}{0ex}}C\right)\left(\sqrt{\frac{{p}^{12}{q}^{\frac{3}{2}}}{64}}{\right)}^{\frac{5}{6}}\phantom{\rule{0ex}{0ex}}D\right)\left(\sqrt{\frac{{p}^{12}{q}^{\frac{3}{2}}}{64}}{\right)}^{\frac{1}{6}}$

erlent00s

Expert

The given expression is
${\frac{{p}^{12}{q}^{3/2}}{64}}^{5/6}$
Recall that:
${a}^{\frac{m}{n}}=\left(\sqrt[n]{a}{\right)}^{m}$
For the given expression,
m=5
n=6
and
$a=\frac{{p}^{12}{q}^{\frac{3}{2}}}{64}$
We substitute all these values to obtain the radical form:
$\left(\frac{{p}^{12}{q}^{\frac{3}{2}}}{64}{\right)}^{\frac{5}{6}}=\left(\sqrt[6]{\frac{{p}^{12}{q}^{3/2}}{64}}{\right)}^{5}$
The correct choice is A.

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