Evaluate (64y^100)^(1/2)

${(64 y^{100})}^{\frac{1}{2}}$

Simplify the expression.

Apply the product rule to $64 y^{100}$ .

$64^{\frac{1}{2}} {(y^{100})}^{\frac{1}{2}}$

Rewrite $64$ as $8^{2}$ .

${(8^{2})}^{\frac{1}{2}} {(y^{100})}^{\frac{1}{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8^{2 (\frac{1}{2})} {(y^{100})}^{\frac{1}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$8^{2 (\frac{1}{2})} {(y^{100})}^{\frac{1}{2}}$

Rewrite the expression.

$8^{1} {(y^{100})}^{\frac{1}{2}}$

Simplify the expression.

Evaluate the exponent.

$8 {(y^{100})}^{\frac{1}{2}}$

Multiply the exponents in ${(y^{100})}^{\frac{1}{2}}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$8 y^{100 (\frac{1}{2})}$

Cancel the common factor of $2$ .

Factor $2$ out of $100$ .

$8 y^{2 (50) \frac{1}{2}}$

Cancel the common factor.

$8 y^{2 \cdot 50 \frac{1}{2}}$

Rewrite the expression.

$8 y^{50}$