Simplify (y^4*2xy)^3

${(y^{4} \cdot 2 x y)}^{3}$

Step 1

Rewrite using the commutative property of multiplication.

${(2 y^{4} (x y))}^{3}$

Step 2

Multiply $y^{4}$ by $y$ by adding the exponents.

Move $y$ .

${(2 (y \cdot y^{4}) x)}^{3}$

Multiply $y$ by $y^{4}$ .

Raise $y$ to the power of $1$ .

${(2 (y^{1} y^{4}) x)}^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(2 y^{1 + 4} x)}^{3}$

Add $1$ and $4$ .

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

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $2 y^{5} x$ .

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

Apply the product rule to $2 y^{5}$ .

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

Step 4

Raise $2$ to the power of $3$ .

$8 {(y^{5})}^{3} x^{3}$

Step 5

Multiply the exponents in ${(y^{5})}^{3}$ .

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

$8 y^{5 \cdot 3} x^{3}$

Multiply $5$ by $3$ .

$8 y^{15} x^{3}$