Simplify (y^3*2^5)^2

${(y^{3} \cdot 2^{5})}^{2}$

Step 1

Raise $2$ to the power of $5$ .

${(y^{3} \cdot 32)}^{2}$

Step 2

Move $32$ to the left of $y^{3}$ .

${(32 \cdot y^{3})}^{2}$

Step 3

Apply the product rule to $32 y^{3}$ .

$32^{2} {(y^{3})}^{2}$

Step 4

Raise $32$ to the power of $2$ .

$1024 {(y^{3})}^{2}$

Step 5

Multiply the exponents in ${(y^{3})}^{2}$ .

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

$1024 y^{3 \cdot 2}$

Multiply $3$ by $2$ .

$1024 y^{6}$