Question

simplify.
\\(\dfrac{2a^{9}b^{2}c^{-8}}{8a^{-3}b^{-4}}\\)
write your answer using only positive exponents.

Explanation:

Step1: Simplify coefficient

$\frac{2}{8} = \frac{1}{4}$

Step2: Simplify $a$-terms (add exponents)

$a^{9 - (-3)} = a^{9+3} = a^{12}$

Step3: Simplify $b$-terms (add exponents)

$b^{2 - (-4)} = b^{2+4} = b^{6}$

Step4: Rewrite $c$-term to positive exponent

$c^{-8} = \frac{1}{c^{8}}$

Step5: Combine all simplified parts

$\frac{1}{4} \cdot a^{12} \cdot b^{6} \cdot \frac{1}{c^{8}}$

Answer:

$\frac{a^{12}b^{6}}{4c^{8}}$