Simplify the Radical Expression ((3^6)/(y^-5))^2

${(\frac{3^{6}}{y^{- 5}})}^{2}$

Step 1

Move $y^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(3^{6} y^{5})}^{2}$

Step 2

Raise $3$ to the power of $6$ .

${(729 y^{5})}^{2}$

Step 3

Apply the product rule to $729 y^{5}$ .

$729^{2} {(y^{5})}^{2}$

Step 4

Raise $729$ to the power of $2$ .

$531441 {(y^{5})}^{2}$

Step 5

Multiply the exponents in ${(y^{5})}^{2}$ .

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

$531441 y^{5 \cdot 2}$

Multiply $5$ by $2$ .

$531441 y^{10}$