Question

express the following fraction in simplest form using only positive expon\frac{(3k^{3})^{3}}{5k^{6}}

Explanation:

Step1: Expand the numerator

Apply power of a product rule: $(ab)^n=a^n b^n$ and power rule: $(a^m)^n=a^{m \cdot n}$
$(3k^3)^3 = 3^3 \cdot (k^3)^3 = 27k^{9}$

Step2: Simplify the fraction

Substitute expanded numerator and divide like terms using $\frac{a^m}{a^n}=a^{m-n}$
$\frac{27k^{9}}{5k^{6}} = \frac{27}{5}k^{9-6} = \frac{27}{5}k^{3}$

Answer:

$\frac{27}{5}k^3$