Certainly! Let's go through the simplification of the given expressions step-by-step.
### First Expression:
[tex]\[
\left(\frac{1}{4}\right)^{-\frac{5}{2}}
\][/tex]
1. Rewrite the fraction with a negative exponent in terms of a reciprocal:
[tex]\[
\left(\frac{1}{4}\right)^{-\frac{5}{2}} = \left(4\right)^{\frac{5}{2}}
\][/tex]
2. Simplify the exponent:
[tex]\[
4^{\frac{5}{2}} = \left(2^2\right)^{\frac{5}{2}} = 2^{2 \cdot \frac{5}{2}} = 2^5
\][/tex]
3. Calculate the power:
[tex]\[
2^5 = 32
\][/tex]
So,
[tex]\[
\left(\frac{1}{4}\right)^{-\frac{5}{2}} = 32
\][/tex]
### Second Expression:
[tex]\[
-\frac{5}{4}
\][/tex]
This expression is already simplified. The fraction [tex]\(-\frac{5}{4}\)[/tex] remains as is:
[tex]\[
-\frac{5}{4} = -1.25
\][/tex]
### Final Results:
[tex]\[
\begin{array}{c}
\left(\frac{1}{4}\right)^{-\frac{5}{2}} = 32 \\
-\frac{5}{4} = -1.25
\end{array}
\][/tex]
Thus, the simplified values for the given expressions are:
[tex]\[
\begin{array}{c}
\left(\frac{1}{4}\right)^{-\frac{5}{2}} = 32 \\
-\frac{5}{4} = -1.25
\end{array}
\][/tex]
