Question

fully simplify using only positive exponents.\\(\frac{12m^{-3}n^{-8}p^{2}}{14m^{-5}n^{-2}p^{-4}}\\)

Explanation:

Step1: Simplify coefficient fraction

$\frac{12}{14} = \frac{6}{7}$

Step2: Simplify $m$ terms (subtract exponents)

$m^{-3 - (-5)} = m^{2}$

Step3: Simplify $n$ terms (subtract exponents)

$n^{-8 - (-2)} = n^{-6} = \frac{1}{n^{6}}$

Step4: Simplify $p$ terms (subtract exponents)

$p^{2 - (-4)} = p^{6}$

Step5: Combine all simplified terms

$\frac{6}{7} \times m^{2} \times \frac{1}{n^{6}} \times p^{6}$

Answer:

$\frac{6m^{2}p^{6}}{7n^{6}}$