Answer
Rule:
$\sqrt[n]{a^{m}}\cdot\sqrt[p]{a^{m}}=\sqrt[np]{a^{m(p+n)}}$
Work Step by Step
Applying the key concept of this section,
$\sqrt[n]{a^{m}}=a^{m/n}, \qquad\sqrt[p]{a^{m}}=a^{m/p}$
$\sqrt[n]{a^{m}}\cdot\sqrt[p]{a^{m}}=a^{m/n}\cdot a^{m/p}$
$=a^{\frac{m}{n}+\frac{m}{p}}\qquad$ ... multiplying powers of the same base
$=a^{\frac{mp+mn}{np}}\qquad$ ... simplify the exponent
$=\sqrt[np]{a^{mp+mn}}\qquad$ ... applied key concept
$=\sqrt[np]{a^{m(p+n)}}$
Rule:
$\sqrt[n]{a^{m}}\cdot\sqrt[p]{a^{m}}=\sqrt[np]{a^{m(p+n)}}$
