Question

express the following fraction in simplest form, only using exponents.
$\frac{-2(p^{-4}y^{4})^{-3}}{6p^{-3}y^{-1}}$

Explanation:

Step1: Simplify coefficient fraction

$\frac{-2}{6} = -\frac{1}{3}$

Step2: Simplify $(p^{-4}y^4)^{-3}$

Use exponent rule $(a^m)^n=a^{mn}$:
$p^{(-4)\times(-3)}y^{4\times(-3)} = p^{12}y^{-12}$

Step3: Combine like base exponents for $p$

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$:
$p^{12 - (-3)} = p^{12+3}=p^{15}$

Step4: Combine like base exponents for $y$

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$:
$y^{-12 - (-1)} = y^{-12+1}=y^{-11}$

Step5: Combine all simplified terms

Multiply coefficient and variable terms together.

Answer:

$-\frac{1}{3}p^{15}y^{-11}$ or $-\frac{p^{15}}{3y^{11}}$