Question

Simplify using exponent rule. Show work please

Answer 1

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^{(1)/(3)}*y^{(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}`

Answer 2

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