Simplify (4xy^2)^3(xy)^5

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

Step 1

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

Apply the product rule to $4 x y^{2}$ .

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

Apply the product rule to $4 x$ .

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

Step 2

Raise $4$ to the power of $3$ .

$64 x^{3} {(y^{2})}^{3} {(x y)}^{5}$

Step 3

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

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

$64 x^{3} y^{2 \cdot 3} {(x y)}^{5}$

Multiply $2$ by $3$ .

$64 x^{3} y^{6} {(x y)}^{5}$

Step 4

Apply the product rule to $x y$ .

$64 x^{3} y^{6} (x^{5} y^{5})$

Step 5

Multiply $x^{3}$ by $x^{5}$ by adding the exponents.

Move $x^{5}$ .

$64 (x^{5} x^{3}) y^{6} y^{5}$

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

$64 x^{5 + 3} y^{6} y^{5}$

Add $5$ and $3$ .

$64 x^{8} y^{6} y^{5}$

Step 6

Multiply $y^{6}$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

$64 x^{8} (y^{5} y^{6})$

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

$64 x^{8} y^{5 + 6}$

Add $5$ and $6$ .

$64 x^{8} y^{11}$