Simplify -8(x^-3y^4)^-5

$- 8 {(x^{- 3} y^{4})}^{- 5}$

Step 1

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

$- 8 {(\frac{1}{x^{3}} y^{4})}^{- 5}$

Step 2

Combine $\frac{1}{x^{3}}$ and $y^{4}$ .

$- 8 {(\frac{y^{4}}{x^{3}})}^{- 5}$

Step 3

Change the sign of the exponent by rewriting the base as its reciprocal.

$- 8 {(\frac{x^{3}}{y^{4}})}^{5}$

Step 4

Apply basic rules of exponents.

Apply the product rule to $\frac{x^{3}}{y^{4}}$ .

$- 8 \frac{{(x^{3})}^{5}}{{(y^{4})}^{5}}$

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

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

$- 8 \frac{x^{3 \cdot 5}}{{(y^{4})}^{5}}$

Multiply $3$ by $5$ .

$- 8 \frac{x^{15}}{{(y^{4})}^{5}}$

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

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

$- 8 \frac{x^{15}}{y^{4 \cdot 5}}$

Multiply $4$ by $5$ .

$- 8 \frac{x^{15}}{y^{20}}$

Step 5

Combine $- 8$ and $\frac{x^{15}}{y^{20}}$ .

$\frac{- 8 x^{15}}{y^{20}}$

Step 6

Move the negative in front of the fraction.

$- \frac{8 x^{15}}{y^{20}}$