Answer:
[tex]\frac{1}{2^{10}} \ and\ \frac{1}{1024}[/tex]
Step-by-step explanation:
Given
[tex](2^{5})^{-2}[/tex]
Required
Find the equivalent;
To find the equivalent of the given expression, we make use of laws of indices;
Using the following law of indices;
[tex](a^m)^n = a^{m*n}[/tex]
So;
[tex](2^{5})^{-2}[/tex] becomes
[tex](2^{5})^{-2} = 2^{5*-2}[/tex]
[tex](2^{5})^{-2} = 2^{-10}[/tex] ------------ This is one equivalent
Solving further;
Using the following law of indices;
[tex]a^{-m} = \frac{1}{a^m}[/tex]
So;
[tex](2^{5})^{-2} = 2^{-10}[/tex] becomes
[tex](2^{5})^{-2} = \frac{1}{2^{10}}[/tex]
[tex]2^10 = 1024[/tex]
Hence;
[tex](2^{5})^{-2} = \frac{1}{1024}[/tex]
Conclusively; the equivalents of [tex](2^{5})^{-2}[/tex] are [tex]\frac{1}{2^{10}} \ and\ \frac{1}{1024}[/tex]
