Question

simplify.
$(2x^{4}y^{-3})^{3}$
write your answer using only positive exponents.

Explanation:

Step1: Apply power of a product rule

$(ab)^n = a^n b^n$, so:
$$(2x^4 y^{-3})^3 = 2^3 \cdot (x^4)^3 \cdot (y^{-3})^3$$

Step2: Simplify each term's exponent

Use $(a^m)^n = a^{m \cdot n}$:
$$2^3 = 8, \quad (x^4)^3 = x^{4 \cdot 3} = x^{12}, \quad (y^{-3})^3 = y^{-3 \cdot 3} = y^{-9}$$
Combine terms:
$$8x^{12}y^{-9}$$

Step3: Convert to positive exponents

Use $a^{-n} = \frac{1}{a^n}$:
$$8x^{12} \cdot \frac{1}{y^9} = \frac{8x^{12}}{y^9}$$

Answer:

$\frac{8x^{12}}{y^9}$