Question

Fiind the value of each of the following:
(i) 3⁻¹ + 4⁻¹
(ii) (3⁰ + 4⁻¹) × 2²
(iii) (3⁻¹ + 4⁻¹ + 5⁻¹)⁰
(iv) ${\left\{{\left(\frac{1}{3}\right)}^{-1}-{\left(\frac{1}{4}\right)}^{-1}\right\}}^{-1}$

Answer 1

(i) We know from the property of powers that for every natural number a, a⁻¹ = 1/a. Then:
---> (a⁻¹ = 1/a)



(ii) We know from the property of powers that for every natural number a, a⁻¹ = 1/a.
Moreover, a⁰ is 1 for every natural number a not equal to 0. Then:

$$\begin{gathered} \left(3^0+4^{-1}\right)\times 2^2 \\ =\left(1+\frac{1}{4}\right)\times 4\left[\mathrm{as},{\mathrm{a}}^{-1}=\frac{1}{\mathrm{a}};{\mathrm{a}}^0=1\right] \\ =\frac{5}{4}\times 4 \\ =5 \end{gathered}$$


(iii) We know from the property of powers that for every natural number a, a⁻¹ = 1/a.
Moreover, a⁰ is 1 for every natural number a not equal to 0. Then:
$(3^{-1}+4^{-1}+5^{-1})=1$ ---> (Ignore the expression inside the bracket and use a⁰ = 1 immediately.)

(iv) We know from the property of powers that for every natural number a, a⁻¹ = 1/a. Then:
---> (a⁻¹ = 1/a)

=$-1$ ---> (a⁻¹ = 1/a)