Question

simplify.
$(3x^{6}y^{-4})^{-3}$
write your answer using only positive exponents.

Explanation:

Step1: Apply power of a product rule

$(ab)^n=a^n b^n$, so:
$$(3x^6 y^{-4})^{-3}=3^{-3} \cdot (x^6)^{-3} \cdot (y^{-4})^{-3}$$

Step2: Simplify each exponent term

Use $(a^m)^n=a^{m \cdot n}$ and $a^{-n}=\frac{1}{a^n}$:
$$3^{-3}=\frac{1}{3^3}=\frac{1}{27}, \quad (x^6)^{-3}=x^{6 \cdot (-3)}=x^{-18}=\frac{1}{x^{18}}, \quad (y^{-4})^{-3}=y^{(-4) \cdot (-3)}=y^{12}$$

Step3: Multiply all simplified terms

$$\frac{1}{27} \cdot \frac{1}{x^{18}} \cdot y^{12} = \frac{y^{12}}{27x^{18}}$$

Answer:

$\frac{y^{12}}{27x^{18}}$