Questions: Simplify. [ left(frac4 m^7 n^48 m^3right)^3 ] Write your answer using only positive exponents.

$Simplify. [ left(frac4 m^7 n^48 m^3right)^3 ] Write your answer using only positive exponents.$

Transcript text: 021 Course Introduction - 202502 MI ALEKS - Taylor Hess - Knowled https://www-awy.aleks.com/alekscgi/x/Isl.exe/1o_u-lgNsikr7j8P3jH- Initial Knowledge Check Question 23 Simplify. \[ \left(\frac{4 m^{7} n^{4}}{8 m^{3}}\right)^{3} \] Write your answer using only positive exponents. $\square$ $\square$ I Don't Know Submit 1 In Search

Solution

Solution Steps

Step 1: Rewrite the Expression

We start with the expression: \[ \left(\frac{4 m^{7} n^{4}}{8 m^{3}}\right)^{3} \]

Step 2: Simplify the Fraction Inside the Parentheses

First, we simplify the fraction: \[ \frac{4 m^{7} n^{4}}{8 m^{3}} = \frac{4}{8} \cdot \frac{m^{7}}{m^{3}} \cdot n^{4} = \frac{1}{2} \cdot m^{7-3} \cdot n^{4} = \frac{1}{2} m^{4} n^{4} \]

Step 3: Raise the Simplified Expression to the Power of 3

Next, we raise the simplified expression to the power of 3: \[ \left(\frac{1}{2} m^{4} n^{4}\right)^{3} = \frac{1^{3}}{2^{3}} \cdot (m^{4})^{3} \cdot (n^{4})^{3} = \frac{1}{8} m^{12} n^{12} \]

Step 4: Write the Final Simplified Expression

Thus, the final simplified expression is: \[ \frac{m^{12} n^{12}}{8} \]