Question

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

Explanation:

Step1: Simplify the coefficient

Simplify the fraction of the coefficients: $\frac{15}{3} = 5$.

Step2: Simplify the variable part using exponent rules

First, 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, we have the fraction $\frac{m^7}{m^4}$. Using the quotient rule of exponents $\frac{a^m}{a^n}=a^{m - n}$ (where $a
eq0$ and $m>n$), we get $m^{7 - 4}=m^3$.

Step3: Combine the coefficient and the variable part

Multiply the simplified coefficient and the simplified variable part: $5\times m^3 = 5m^3$.

Answer:

$5m^3$