Question

express the following fraction in simplest form, only using positive exponents.\\(\frac{(3k^{-3})^{5}}{-4k^{-10}}\\)

Explanation:

Step1: Expand numerator via exponent rule

$(3k^{-3})^5 = 3^5 \cdot (k^{-3})^5 = 243k^{-15}$

Step2: Rewrite negative exponents as positive

$\frac{243k^{-15}}{-4k^{-10}} = \frac{243}{-4} \cdot \frac{1}{k^{15}} \cdot k^{10}$

Step3: Simplify variable terms

$\frac{243}{-4} \cdot k^{10-15} = -\frac{243}{4}k^{-5} = -\frac{243}{4k^5}$

Answer:

$-\frac{243}{4k^5}$