Let's solve the given expression step by step:
[tex]\[
\left(\frac{27}{125}\right)^{\frac{2}{3}} \times \left(\frac{9}{25}\right)^{\frac{-3}{2}}
\][/tex]
### Step 1: Simplify the fractions separately
First, let's evaluate the fraction [tex]\(\frac{27}{125}\)[/tex]:
The fraction [tex]\(\frac{27}{125}\)[/tex] can be simplified to:
[tex]\[
\frac{27}{125} = 0.216
\][/tex]
Next, let's evaluate the fraction [tex]\(\frac{9}{25}\)[/tex]:
The fraction [tex]\(\frac{9}{25}\)[/tex] can be simplified to:
[tex]\[
\frac{9}{25} = 0.36
\][/tex]
### Step 2: Compute the powers of each fraction
#### Power Calculation for [tex]\(\frac{27}{125}\)[/tex]
Now, let's compute [tex]\( \left(\frac{27}{125}\right)^{\frac{2}{3}} \)[/tex]:
[tex]\[
0.216^{\frac{2}{3}} = 0.36000000000000004
\][/tex]
#### Power Calculation for [tex]\(\frac{9}{25}\)[/tex]
Next, let's compute [tex]\( \left(\frac{9}{25}\right)^{\frac{-3}{2}} \)[/tex]:
[tex]\[
0.36^{-\frac{3}{2}} = 4.62962962962963
\][/tex]
### Step 3: Multiply the results
Finally, multiply these computed values together:
[tex]\[
0.36000000000000004 \times 4.62962962962963 = 1.666666666666667
\][/tex]
### Conclusion
Thus, the value of the expression [tex]\(\left(\frac{27}{125}\right)^{\frac{2}{3}} \times \left(\frac{9}{25}\right)^{\frac{-3}{2}}\)[/tex] is:
[tex]\[
1.666666666666667
\][/tex]
