Question

express the following fraction in simplest form, only using positive exponents.\\(\frac{-5(r^{3})^{2}}{5r^{10}}\\)

Explanation:

Step1: Simplify the numerator's exponent

Apply power rule: $(r^3)^2 = r^{3\times2}=r^6$, so numerator becomes $-5r^6$

Step2: Simplify the constant terms

Divide constants: $\frac{-5}{5}=-1$

Step3: Simplify the variable terms

Apply quotient rule: $\frac{r^6}{r^{10}}=r^{6-10}=r^{-4}$

Step4: Convert to positive exponents

Rewrite $r^{-4}$ as $\frac{1}{r^4}$

Answer:

$-\frac{1}{r^4}$