Question

simplify.
\\(\left(\frac{m^{7}n^{6}}{m^{4}n}\
ight)^{5}\\)
write your answer using only po

Explanation:

Step1: Simplify the fraction inside the parentheses

First, use the quotient rule for exponents, which states that $\frac{a^m}{a^n} = a^{m - n}$. For the $m$ terms: $\frac{m^7}{m^4} = m^{7 - 4} = m^3$. For the $n$ terms: $\frac{n^6}{n^1} = n^{6 - 1} = n^5$. So the expression inside the parentheses simplifies to $m^3n^5$.

Step2: Apply the power of a product rule

Now, raise the simplified expression to the 5th power. The power of a product rule states that $(ab)^n = a^n b^n$. So, $(m^3n^5)^5 = (m^3)^5 \cdot (n^5)^5$.

Step3: Apply the power of a power rule

The power of a power rule states that $(a^m)^n = a^{m \cdot n}$. For the $m$ term: $(m^3)^5 = m^{3 \cdot 5} = m^{15}$. For the $n$ term: $(n^5)^5 = n^{5 \cdot 5} = n^{25}$.

Answer:

$m^{15}n^{25}$