Question

complete the steps to simplify (left(y^{\frac{4}{3}} cdot y^{\frac{2}{3}}
ight)^{-\frac{1}{2}}). apply the product of powers property to the expression inside the parentheses, then choose the equivalent expression. (left(y^{\frac{4}{3}}
ight)^{-\frac{1}{2}}) (left(y^{2}
ight)^{-\frac{1}{2}}) (left(y^{\frac{2}{3}}
ight)^{-\frac{1}{2}})

Explanation:

Step1: Apply product of powers

The product of powers property states that \(a^m \cdot a^n = a^{m + n}\). For \(y^{\frac{4}{3}} \cdot y^{\frac{2}{3}}\), we add the exponents: \(\frac{4}{3}+\frac{2}{3}=\frac{6}{3} = 2\). So the expression inside the parentheses becomes \(y^2\).

Step2: Substitute back

Substitute \(y^2\) back into the original expression, we get \((y^2)^{-\frac{1}{2}}\).

Answer:

\(\boldsymbol{(y^2)^{-\frac{1}{2}}}\) (which corresponds to the middle option)