which expression is equivalent to $(64y^{100})^{\frac{1}{2}}$?\n$8y^{10}$\n$8y^{50}$\n$32y^{10}$\n$32y^{50}$

Explanation:

Step1: Apply the power - of - a - product rule ((ab)^n=a^n\times b^n)

[ \begin{align*} (64y^{100})^{\frac{1}{2}}&=64^{\frac{1}{2}}\times(y^{100})^{\frac{1}{2}} \end{align*} ]

Step2: Simplify (64^{\frac{1}{2}})

Since (a^{\frac{1}{2}}=\sqrt{a}), then (64^{\frac{1}{2}}=\sqrt{64} = 8)

Step3: Simplify ((y^{100})^{\frac{1}{2}})

Using the power - of - a - power rule ((a^m)^n=a^{mn}), we have ((y^{100})^{\frac{1}{2}}=y^{100\times\frac{1}{2}}=y^{50})

Answer:

(8y^{50})