Evaluate (x^3)^-3(-2y^5)^4

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

Step 1

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

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

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

Multiply $3$ by $- 3$ .

$x^{- 9} {(- 2 y^{5})}^{4}$

Step 2

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

$\frac{1}{x^{9}} {(- 2 y^{5})}^{4}$

Step 3

Simplify the expression.

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

$\frac{1}{x^{9}} ({(- 2)}^{4} {(y^{5})}^{4})$

Rewrite using the commutative property of multiplication.

${(- 2)}^{4} \frac{1}{x^{9}} {(y^{5})}^{4}$

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

$16 \frac{1}{x^{9}} {(y^{5})}^{4}$

Step 4

Combine $16$ and $\frac{1}{x^{9}}$ .

$\frac{16}{x^{9}} {(y^{5})}^{4}$

Step 5

Multiply the exponents in ${(y^{5})}^{4}$ .

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

$\frac{16}{x^{9}} y^{5 \cdot 4}$

Multiply $5$ by $4$ .

$\frac{16}{x^{9}} y^{20}$

Step 6

Combine $\frac{16}{x^{9}}$ and $y^{20}$ .

$\frac{16 y^{20}}{x^{9}}$