Simplify (2x^7y)^2(y^5)^3

${(2 x^{7} y)}^{2} {(y^{5})}^{3}$

Step 1

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

Apply the product rule to $2 x^{7} y$ .

${(2 x^{7})}^{2} y^{2} {(y^{5})}^{3}$

Apply the product rule to $2 x^{7}$ .

$2^{2} {(x^{7})}^{2} y^{2} {(y^{5})}^{3}$

Step 2

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

$4 {(x^{7})}^{2} y^{2} {(y^{5})}^{3}$

Step 3

Multiply the exponents in ${(x^{7})}^{2}$ .

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

$4 x^{7 \cdot 2} y^{2} {(y^{5})}^{3}$

Multiply $7$ by $2$ .

$4 x^{14} y^{2} {(y^{5})}^{3}$

Step 4

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

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

$4 x^{14} y^{2} y^{5 \cdot 3}$

Multiply $5$ by $3$ .

$4 x^{14} y^{2} y^{15}$

Step 5

Multiply $y^{2}$ by $y^{15}$ by adding the exponents.

Move $y^{15}$ .

$4 x^{14} (y^{15} y^{2})$

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

$4 x^{14} y^{15 + 2}$

Add $15$ and $2$ .

$4 x^{14} y^{17}$