Answer:
[tex]\frac{r^{15}}{512}[/tex]
Step-by-step explanation:
Given
[tex](8r^{-5})^{-3}[/tex]
Required
Simplify
This can be simplified using the following law of indices;
[tex](ab)^n = a^{n}b^{n}[/tex]
The equation becomes
[tex](8^{-3})(r^{-5})^{-3}[/tex]
Express [tex]8^{-3}[/tex] as a fraction
[tex](\frac{1}{8^{3}})(r^{-5})^{-3}[/tex]
Simplify [tex]8^3[/tex]
[tex](\frac{1}{8*8*8})(r^{-5})^{-3}[/tex]
[tex](\frac{1}{512})(r^{-5})^{-3}[/tex]
The expression can further be simplified using the following law of indices;
[tex](a^m)^n = a^{mn}[/tex]
[tex](\frac{1}{512})(r^{-5})^{-3}[/tex] becomes
[tex](\frac{1}{512})(r^{-5*-3})[/tex]
[tex](\frac{1}{512})(r^{15})[/tex]
[tex]\frac{r^{15}}{512}[/tex]
Hence, the solution to [tex](8r^{-5})^{-3}[/tex] is [tex]\frac{r^{15}}{512}[/tex]
