Question

Question 94

Solve the following:

Express $\frac{27}{64}$ and $\frac{-27}{64}$ as powers of a rational number.

Answer 1

$\because 27=3\times 3\times 3=3^3,(-27)=(-3)\times (-3)\times (-3)=(-3{)}^{3}and64=4\times 4\times 4=4^3\therefore \frac{27}{64}=\frac{3^3}{4^3}={\left(\frac{3}{4}\right)}^{4}and\frac{-27}{64}=\frac{(-3{)}^3}{(4{)}^3}={\left(\frac{-3}{4}\right)}^3$