Class 9 Math Exercise 1.6 | Question 3

Question 3: Simplify:
(i) \2^\frac{2}{3} × 2^\frac{1}{5})
(ii) \\left[\frac{1}{3^3}\right]^7)
(iii) \\frac{\left(11^\frac{1}{2}\right)}{\left(11^\frac{1}{4}\right)})
(iv) \125^\frac{-1}{3})

Explanatory Answer | Exercise 1.6 Question 3

(i) Simplify \2^\frac{2}{3} × 2^\frac{1}{5})

Law of Exponent Used: a^p × a^q = a^{(p + q)}
\2^\frac{2}{3} × 2^\frac{1}{5}) = \2^{\frac{2}{3} + \frac{1}{5}})
= \2^{\frac{10 + 3}{15}})
= \2^\frac{13}{15})

(ii) Simplify \\left[\frac{1}{3^3}\right]^7)

Laws of Exponent Used:1. (a^p)^q = a^pq and 2. \\frac{1}{a^p} = a^{-p})
\\left[\frac{1}{3^3}\right]^7) = \\frac{1^7}{3^{(3 × 7)}})
= \\frac{1}{3^{21}})
= 3^(-21)

(iii) Simplify \\frac{\left(11^\frac{1}{2}\right)}{\left(11^\frac{1}{4}\right)})

Law of Exponent Used: a^p ÷ a^q = a^{(p - q)}
\\frac{\left(11^\frac{1}{2}\right)}{\left(11^\frac{1}{4}\right)}) = \11^{\frac{1}{2}} ÷ 11^{\frac{1}{4}})
= \11^{(\frac{1}{2} - \frac{1}{4})})
= \11^{\frac{1}{4}})

(iv) Simplify \7^\frac{1}{2}) × \8^\frac{1}{2})

Law of Exponent Used: a^p × b^p = (ab)^p
\7^\frac{1}{2}) × \8^\frac{1}{2}) = \{(7 × 8)}^{\frac{1}{2}})
= \56^\frac{1}{2})