Sure, let's simplify the given expression step by step.
### Step 1: Simplify the first expression:
[tex]\[
\left(\frac{m^{-1} m^5}{m^{-2}}\right)^{-3}
\][/tex]
First, simplify the expression inside the parentheses:
Combine the powers of [tex]\(m\)[/tex] inside the fraction:
[tex]\[
m^{-1} \cdot m^5 = m^{-1 + 5} = m^4
\][/tex]
Now we have:
[tex]\[
\left(\frac{m^4}{m^{-2}}\right)^{-3}
\][/tex]
Next, simplify the fraction:
[tex]\[
\frac{m^4}{m^{-2}} = m^{4 - (-2)} = m^{4 + 2} = m^6
\][/tex]
Now, we raise this to the power of [tex]\(-3\)[/tex]:
[tex]\[
(m^6)^{-3} = m^{6 \cdot (-3)} = m^{-18}
\][/tex]
So, the simplified form of the first expression is:
[tex]\[
m^{-18}
\][/tex]
### Step 2: Simplify the second expression:
[tex]\[
-\frac{3 m^4}{m^{-2}}
\][/tex]
Simplify the fraction by combining the powers of [tex]\(m\)[/tex]:
[tex]\[
-\frac{3 m^4}{m^{-2}} = -3 \cdot m^{4 - (-2)} = -3 \cdot m^{4 + 2} = -3 \cdot m^6
\][/tex]
So, the simplified form of the second expression is:
[tex]\[
-3m^6
\][/tex]
### Final Answer:
Thus, after simplifying the given expressions, we get:
1. [tex]\(\left(\frac{m^{-1} m^5}{m^{-2}}\right)^{-3}\)[/tex] simplifies to [tex]\(\boxed{m^{-18}}\)[/tex]
2. [tex]\(-\frac{3 m^4}{m^{-2}}\)[/tex] simplifies to [tex]\(\boxed{-3m^6}\)[/tex]
