Simplify -(2xy^3)^-5

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

Step 1

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

$- \frac{1}{{(2 x y^{3})}^{5}}$

Step 2

Simplify the denominator.

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

$- \frac{1}{{(2 x)}^{5} {(y^{3})}^{5}}$

Apply the product rule to $2 x$ .

$- \frac{1}{2^{5} x^{5} {(y^{3})}^{5}}$

Raise $2$ to the power of $5$ .

$- \frac{1}{32 x^{5} {(y^{3})}^{5}}$

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

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

$- \frac{1}{32 x^{5} y^{3 \cdot 5}}$

Multiply $3$ by $5$ .

$- \frac{1}{32 x^{5} y^{15}}$