Question

Evaluate:

(i) (5/9)^-2 x (3/5)^-3 x (3/5)⁰

(ii) (-3/5)^-4 x (-2/5)²

(iii) (-2/3)^-3 x (-2/3)^-2

Answer 1

(i) \((\frac{5}{9})^{-2}\times(\frac{3}{5})^{-3}\times(\frac{3}{5})^0\)

First we add the power of the same base,

= \((\frac{5}{9})^{-2}\times(\frac{3}{5})^{-3}+0\)

Convert the powers in to positive numbers,

= \(\frac{9^2}{5^2}\times\frac{5^3}{3^3}\)

= \(\frac{(3^2)}{5^2}\times\frac{5^3}{3^3}\)

= (3(^4-3)) × (5(^3-2)) = 3 × 15 = 15