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

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

Step 1

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

$\frac{1}{{(4 x^{2} y^{5})}^{2}}$

Step 2

Simplify the denominator.

Apply the product rule to $4 x^{2} y^{5}$ .

$\frac{1}{{(4 x^{2})}^{2} {(y^{5})}^{2}}$

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

$\frac{1}{4^{2} {(x^{2})}^{2} {(y^{5})}^{2}}$

Raise $4$ to the power of $2$ .

$\frac{1}{16 {(x^{2})}^{2} {(y^{5})}^{2}}$

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

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

$\frac{1}{16 x^{2 \cdot 2} {(y^{5})}^{2}}$

Multiply $2$ by $2$ .

$\frac{1}{16 x^{4} {(y^{5})}^{2}}$

Multiply the exponents in ${(y^{5})}^{2}$ .

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

$\frac{1}{16 x^{4} y^{5 \cdot 2}}$

Multiply $5$ by $2$ .

$\frac{1}{16 x^{4} y^{10}}$