Simplify (x^5y^8)^5(4xy)

${(x^{5} y^{8})}^{5} (4 x y)$

Step 1

Rewrite using the commutative property of multiplication.

$4 {(x^{5} y^{8})}^{5} x y$

Step 2

Apply the product rule to $x^{5} y^{8}$ .

$4 ({(x^{5})}^{5} {(y^{8})}^{5}) x y$

Step 3

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

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

$4 (x^{5 \cdot 5} {(y^{8})}^{5}) x y$

Multiply $5$ by $5$ .

$4 (x^{25} {(y^{8})}^{5}) x y$

Step 4

Multiply $x^{25}$ by $x$ by adding the exponents.

Move $x$ .

$4 (x \cdot x^{25} {(y^{8})}^{5}) y$

Multiply $x$ by $x^{25}$ .

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

$4 (x^{1} x^{25} {(y^{8})}^{5}) y$

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

$4 (x^{1 + 25} {(y^{8})}^{5}) y$

Add $1$ and $25$ .

$4 (x^{26} {(y^{8})}^{5}) y$

Step 5

Multiply the exponents in ${(y^{8})}^{5}$ .

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

$4 (x^{26} y^{8 \cdot 5}) y$

Multiply $8$ by $5$ .

$4 (x^{26} y^{40}) y$

Step 6

Multiply $y^{40}$ by $y$ by adding the exponents.

Move $y$ .

$4 (x^{26} (y \cdot y^{40}))$

Multiply $y$ by $y^{40}$ .

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

$4 (x^{26} (y^{1} y^{40}))$

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

$4 (x^{26} y^{1 + 40})$

Add $1$ and $40$ .

$4 (x^{26} y^{41})$

$4 x^{26} y^{41}$