It is required to prove:
[tex](8^{-2})^3=\frac{1}{8^6}[/tex]To prove without using the exponent law (x^a)^b = x^ab
So, find the value of each side
so,
The left side =
[tex](8^{-2})^3=(\frac{1}{8^2})^3=(\frac{1}{64})^3=\frac{1^3}{64^3}=\frac{1}{64\cdot64\cdot64}=\frac{1}{262,144}[/tex]The right side =
[tex]\frac{1}{8^6}=\frac{1}{8\cdot8\cdot8\cdot8\cdot8\cdot8}=\frac{1}{262,144}[/tex]so, the left side = the right side
