Class 9 Math Exercise 1.6 | Question 2

Question 2: Find:
(i) \9^\frac{3}{2})
(ii) \32^\frac{2}{5})
(iii) \16^\frac{3}{4})
(iv) \125^\frac{-1}{3})

Explanatory Answer | Exercise 1.6 Question 2

(i) \9^\frac{3}{2})

\9^\frac{3}{2}) = (3²)^{\\frac{3}{2})}
= 3^{(2 × \\frac{3}{2}))}
= 3³ = 27

(ii) \32^\frac{2}{5})

\32^\frac{2}{5}) = (2⁵)^{\\frac{2}{5})}
= 2^{(5 × \\frac{2}{5}))}
= 2² = 4

(iii) \16^\frac{3}{4})

\16^\frac{3}{4}) = (2⁴)^{\\frac{3}{4})}
= 2^{(4 × \\frac{3}{4}))}
= 2³ = 8

(iv) \125^\frac{-1}{3})

\125^\frac{-1}{3}) = (5³)^{\\frac{-1}{3})}
= 5^{(3 × \\frac{-1}{3}))}
= 5^-1 = \\frac{1}{5})