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

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

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(2 x^{3} y^{7})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $2 x^{3} y^{7}$ .

$\frac{1}{{(2 x^{3})}^{2} {(y^{7})}^{2}}$

Apply the product rule to $2 x^{3}$ .

$\frac{1}{2^{2} {(x^{3})}^{2} {(y^{7})}^{2}}$

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

$\frac{1}{4 {(x^{3})}^{2} {(y^{7})}^{2}}$

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

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

$\frac{1}{4 x^{3 \cdot 2} {(y^{7})}^{2}}$

Multiply $3$ by $2$ .

$\frac{1}{4 x^{6} {(y^{7})}^{2}}$

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

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

$\frac{1}{4 x^{6} y^{7 \cdot 2}}$

Multiply $7$ by $2$ .

$\frac{1}{4 x^{6} y^{14}}$