Evaluate (-2x^5y^7)^3+7x^15y^21

${(- 2 x^{5} y^{7})}^{3} + 7 x^{15} y^{21}$

Simplify each term.

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

Apply the product rule to $- 2 x^{5} y^{7}$ .

${(- 2 x^{5})}^{3} {(y^{7})}^{3} + 7 x^{15} y^{21}$

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

${(- 2)}^{3} {(x^{5})}^{3} {(y^{7})}^{3} + 7 x^{15} y^{21}$

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

$- 8 {(x^{5})}^{3} {(y^{7})}^{3} + 7 x^{15} y^{21}$

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

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

$- 8 x^{5 \cdot 3} {(y^{7})}^{3} + 7 x^{15} y^{21}$

Multiply $5$ by $3$ .

$- 8 x^{15} {(y^{7})}^{3} + 7 x^{15} y^{21}$

Multiply the exponents in ${(y^{7})}^{3}$ .

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

$- 8 x^{15} y^{7 \cdot 3} + 7 x^{15} y^{21}$

Multiply $7$ by $3$ .

$- 8 x^{15} y^{21} + 7 x^{15} y^{21}$

Add $- 8 x^{15} y^{21}$ and $7 x^{15} y^{21}$ .

$- x^{15} y^{21}$