Question

Simplify using exponent rule. Show work please

Answer 1

$\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left( 8y \right)^{\frac{1}{3}}\implies \left(8^{\frac{1}{3}}y^{\frac{1}{3}} \right)\implies (2^3)^{\frac{1}{3}}y^{\frac{1}{3}}\implies 2^{3\cdot \frac{1}{3}}y^{\frac{1}{3}}\implies 2^1y^{\frac{1}{3}}\implies 2\sqrt[3]{y}$

Answer 2

Answer:

Step-by-step explanation:

Remember that the exponent is not only on the variable in a situation like this, it is also on the constant.  We can rewrite as

$8^{\frac{1}{3}}*y^{\frac{1}{3}}$

A one-third power is the same thing as

$\sqrt[3]{8}*\sqrt[3]{y}$

The cubed root of 8 is 2 (2 * 2 * 2 = 8) so the simplfication of the exponential term is

$2\sqrt[3]{y}$