Question

algebra: concepts and connections - plc
multiplying and dividing rational expressions
what is the quotient of (\frac{m^{6}}{5} div \frac{5}{m^{2}})? assume (m
eq 0).
options: (m^{4}), (m^{3}), (\frac{m^{8}}{5}), (\frac{m^{6}}{25})

Explanation:

Step1: Rewrite division as multiplication

$\frac{m^6}{5} \div \frac{5}{m^2} = \frac{m^6}{5} \times \frac{m^2}{5}$

Step2: Multiply numerators and denominators

$\frac{m^6 \times m^2}{5 \times 5}$

Step3: Simplify using exponent rule

$\frac{m^{6+2}}{25} = \frac{m^8}{25}$

Answer:

$\frac{m^8}{25}$