EXERCISE SOLUTION-0.5, Calculus Book

Q.01-02 Simplify the expression without using a calculating utility. Solution: 1.  (a) $$\quad-8^{2 / 3}=-\left(2^3\right)^{2 / 3}=-2^2=-4$$ (b) $$\quad(-8)^{2 / 3}=\left[(-8)^2\right]^{1 / 3}=[16]^{1 / 3}=\left(4^3\right)^{1 / 3}=4$$ (c) $$8^{-2 / 3}=\left(2^3\right)^{-2 / 3}=(2)^{-2}=\frac{1}{2^2}=\frac{1}{4}$$ 2. (a) $$2^{-4}=\frac{1}{2^4}=\frac{1}{16}$$ (b) $$\quad 4^{1.5}=4^{15 / 10}=4^{3 / 2}=4^{3 / 2}=\left(2^2\right)^{3 / 2}=2^3=8$$ (c) $$9^{-0.5}=9^{-5 / 10}=\left(3^2\right)^{-1 / 2}=(3)^{-1}=\frac{1}{3}$$ Q.05 Find … Read more