Let's simplify the given expression step-by-step.
The expression to simplify is:
[tex]\[
\left(m^4\right)^{\frac{3}{8}}
\][/tex]
1. Using the power of a power property:
When you raise a power to another power, you multiply the exponents. The property states:
[tex]\[
(a^m)^n = a^{m \cdot n}
\][/tex]
2. Apply this property to our expression:
[tex]\[
\left(m^4\right)^{\frac{3}{8}} = m^{4 \cdot \frac{3}{8}}
\][/tex]
3. Multiply the exponents:
[tex]\[
4 \cdot \frac{3}{8} = \frac{4 \cdot 3}{8} = \frac{12}{8} = \frac{3}{2}
\][/tex]
Thus, the simplified expression is:
[tex]\[
m^{\frac{3}{2}}
\][/tex]
Therefore, the answer is:
[tex]\(\boxed{m^{0.375}}\)[/tex]
