Question

simplify,
\\(\left(4x^{4}y^{-3}\
ight)^{-3}\\)
write your answer using only positive exponents.

Explanation:

Step1: Apply power of a product rule

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

Step2: Simplify each exponent term

$$4^{-3} = \frac{1}{4^3} = \frac{1}{64}, \quad (x^4)^{-3} = x^{4 \times (-3)} = x^{-12}, \quad (y^{-3})^{-3} = y^{(-3) \times (-3)} = y^{9}$$

Step3: Rewrite negative exponents positively

$$x^{-12} = \frac{1}{x^{12}}$$

Step4: Combine all terms

$$\frac{1}{64} \cdot \frac{1}{x^{12}} \cdot y^{9} = \frac{y^9}{64x^{12}}$$

Answer:

$\frac{y^9}{64x^{12}}$