Question

simplify (sqrt{y^4})

Explanation:

Step1: Rewrite the radical as exponent

Recall that $\sqrt{a}=a^{\frac{1}{2}}$, so $\sqrt{y^{4}}=(y^{4})^{\frac{1}{2}}$.

Step2: Apply exponent power rule

Using the power - of - a - power rule $(a^{m})^{n}=a^{m\times n}$, here $a = y$, $m = 4$, $n=\frac{1}{2}$. Then $(y^{4})^{\frac{1}{2}}=y^{4\times\frac{1}{2}}$.

Step3: Simplify the exponent

Calculate $4\times\frac{1}{2}=2$, so $y^{4\times\frac{1}{2}} = y^{2}$.

Answer:

$y^{2}$