Question

simplify.\\(
\frac{(2n^6)^3}{(8n^3)^2}
\\)write your answer using only positive exponents.

Explanation:

Step1: Expand numerator via power rule

$(2n^6)^3 = 2^3 \cdot (n^6)^3 = 8n^{18}$

Step2: Expand denominator via power rule

$(8n^3)^2 = 8^2 \cdot (n^3)^2 = 64n^{6}$

Step3: Simplify the fraction

$\frac{8n^{18}}{64n^{6}} = \frac{8}{64} \cdot n^{18-6}$

Step4: Compute coefficients and exponents

$\frac{8}{64} = \frac{1}{8}$, $n^{18-6}=n^{12}$

Answer:

$\frac{n^{12}}{8}$