Simplify (-7x^3y^4)^2(x^2y^5)

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

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

Apply the product rule to $- 7 x^{3} y^{4}$ .

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

Apply the product rule to $- 7 x^{3}$ .

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

Raise $- 7$ to the power of $2$ .

$49 {(x^{3})}^{2} {(y^{4})}^{2} (x^{2} y^{5})$

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

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

$49 x^{3 \cdot 2} {(y^{4})}^{2} (x^{2} y^{5})$

Multiply $3$ by $2$ .

$49 x^{6} {(y^{4})}^{2} (x^{2} y^{5})$

Multiply $x^{6}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$49 (x^{2} x^{6}) {(y^{4})}^{2} y^{5}$

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

$49 x^{2 + 6} {(y^{4})}^{2} y^{5}$

Add $2$ and $6$ .

$49 x^{8} {(y^{4})}^{2} y^{5}$

Multiply the exponents in ${(y^{4})}^{2}$ .

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

$49 x^{8} y^{4 \cdot 2} y^{5}$

Multiply $4$ by $2$ .

$49 x^{8} y^{8} y^{5}$

Multiply $y^{8}$ by $y^{5}$ by adding the exponents.

Move $y^{5}$ .

$49 x^{8} (y^{5} y^{8})$

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

$49 x^{8} y^{5 + 8}$

Add $5$ and $8$ .

$49 x^{8} y^{13}$