Question

simplify.
$(-3x^{-5}y^{3})^{4}$
write your answer using only positive exponents.

Explanation:

Step1: Apply power of a product rule

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

Step2: Calculate each term's power

$$(-3)^4=81,\ (x^{-5})^4=x^{-20},\ (y^3)^4=y^{12}$$

Step3: Convert negative exponent to positive

$$x^{-20}=\frac{1}{x^{20}}$$

Step4: Combine all terms

$$81 \cdot \frac{1}{x^{20}} \cdot y^{12} = \frac{81y^{12}}{x^{20}}$$

Answer:

$\frac{81y^{12}}{x^{20}}$