Question

Which expression correctly simplifies (312415)56?

Answer 1

Answer:

$\sf C)\quad \large\text{ \dfrac{3^{\frac{5}{12}}}{4^{\frac{1}{6}}} }$

Step-by-step explanation:

Given expression:

$\large\text{ \left(\dfrac{3^{\frac{1}{2}}}{4^{\frac{1}{5}}}\right)^\frac{5}{6} }$

$\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:$

$\large\text{ \implies \dfrac{\left(3^{\frac{1}{2}}\right)^\frac{5}{6}}{\left(4^{\frac{1}{5}}\right)^\frac{5}{6}} }$

$\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:$

$\large\text{ \implies \dfrac{3^{(\frac{1}{2}\times \frac{5}{6})}}{4^{(\frac{1}{5}\times \frac{5}{6})}} }$

Simplify:

$\large\text{ \implies \dfrac{3^{\frac{5}{12}}}{4^{\frac{1}{6}}} }$

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