Answer :
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]
### 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]
