1. (1/125)^-2/3
Here are the steps in simplifying the given term.
a. Make the exponent positive by getting the reciprocal of the base.
[tex](\frac{1}{125})^{-\frac{2}{3}}\Rightarrow(125)^{\frac{2}{3}}[/tex]
b. Get the cube root of 125.
[tex]\sqrt[3]{125}=5[/tex]
c. Square the result in step b.
[tex]5^2=5\times5=25[/tex]
Therefore, (1/125)^-2/3 = 25.
2. 64^-2/3
To simplify this, we follow the same steps shown above.
a. Again, make the exponent positive by getting the reciprocal of the base.
[tex]64^{-\frac{2}{3}}\Rightarrow(\frac{1}{64})^{\frac{2}{3}}[/tex]
b. Get the cube root of 1/64.
[tex]\sqrt[3]{\frac{1}{64}}=\frac{1}{4}[/tex]
c. Square the result in step b.
[tex](\frac{1}{4})^2=\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}[/tex]
Hence, 64^-2/3 = 1/16.
