Question

express the following fraction in simplest form, only using positive exponents.\\(\frac{15m^{7}}{3(m^{2})^{2}}\\)

Explanation:

Step1: Simplify the coefficient and the exponent of \(m\) in the denominator

First, simplify the coefficient: \(\frac{15}{3} = 5\). Then, simplify \((m^{2})^{2}\) using the power - of - a - power rule \((a^{m})^{n}=a^{mn}\). So, \((m^{2})^{2}=m^{2\times2}=m^{4}\). Now the expression becomes \(\frac{5m^{7}}{m^{4}}\).

Step2: Simplify the fraction with the same base

When dividing two powers with the same base \(a\) (here \(a = m\)), we use the rule \(\frac{a^{m}}{a^{n}}=a^{m - n}\) (\(a
eq0\)). So, \(\frac{m^{7}}{m^{4}}=m^{7 - 4}=m^{3}\). Combining with the coefficient 5, we get \(5m^{3}\).

Answer:

\(5m^{3}\)