Question

which expression is equivalent to \\(\frac{18a^{6}b^{-6}c^{4}}{4a^{-2}b^{-3}c^{3}}\\)?

\\(\frac{9a^{8}c}{2b^{3}}\\) \\(\frac{12a^{4}c}{b^{9}}\\)

option 1 option 2

\\(\frac{9b^{3}c}{2a^{6}}\\) \\(\frac{9a^{4}b^{3}c}{2}\\)

option 3 option 4

Explanation:

Step1: Simplify coefficients

$\frac{18}{4} = \frac{9}{2}$

Step2: Simplify $a$-terms

$a^{6 - (-2)} = a^{6+2}=a^8$

Step3: Simplify $b$-terms

$b^{-6 - (-3)} = b^{-6+3}=b^{-3}=\frac{1}{b^3}$

Step4: Simplify $c$-terms

$c^{4 - 3}=c^1=c$

Step5: Combine all simplified parts

$\frac{9}{2} \times a^8 \times \frac{1}{b^3} \times c = \frac{9a^8c}{2b^3}$

Answer:

Option 1: $\frac{9a^8c}{2b^3}$