Express each of the following exponential expressions as a rational number. ${(\frac{1}{2})}^{(- 1)} + {(\frac{2}{3})}^{(- 2)} - {(\frac{3}{4})}^{(- 3)}$

Open in App

Solution

${(\frac{1}{2})}^{- 1} + {(\frac{2}{3})}^{- 2} - {(\frac{3}{4})}^{- 3}$
$\Rightarrow 2 + {(\frac{3}{2})}^{2} - {(\frac{4}{3})}^{3}$
$\Rightarrow 2 + \frac{9}{4} - \frac{64}{27}$
$\Rightarrow \frac{216 + 243 - 256}{108} = \frac{203}{108}$ .

Suggest Corrections

Similar questions

Q. Express each of the following exponential expressions as a rational number.

{(\frac{2}{5})}^{(- 3)}

Q. Express each of the following exponential expressions as a rational number.

{(\frac{4}{5})}^{10} \times {[{(\frac{4}{5})}^{2}]}^{3} \div {[{(\frac{4}{5})}^{4}]}^{4}

Q. Simplify each of the following and express each as a rational number:

{(\frac{- 1}{2})}^{5} \times 2^{3} \times {(\frac{3}{4})}^{2}

Q. Simplify each of the following and express each as a rational number:

{(\frac{3}{2})}^{4} \times {(\frac{1}{5})}^{2}

Express each of the following as a rational number in the form $\frac{p}{q} :$

$(i) 6^{- 1} (i i) (- 7)^{- 1} (i i i) {(\frac{1}{4})}^{- 1} (i v) (- 4)^{- 1} \times {(\frac{- 3}{2})}^{- 1} (v) {(\frac{3}{5})}^{- 1} \times {(\frac{5}{2})}^{- 1}$

Join BYJU'S Learning Program

Express each of the following exponential expressions as a rational number. (12)(−1)+(23)(−2)−(34)(−3)

(12)−1+(23)−2−(34)−3⇒2+(32)2−(43)3⇒2+94−6427⇒216+243−256108=203108.

Express each of the following exponential expressions as a rational number. ${(\frac{1}{2})}^{(- 1)} + {(\frac{2}{3})}^{(- 2)} - {(\frac{3}{4})}^{(- 3)}$

${(\frac{1}{2})}^{- 1} + {(\frac{2}{3})}^{- 2} - {(\frac{3}{4})}^{- 3}$
$\Rightarrow 2 + {(\frac{3}{2})}^{2} - {(\frac{4}{3})}^{3}$
$\Rightarrow 2 + \frac{9}{4} - \frac{64}{27}$
$\Rightarrow \frac{216 + 243 - 256}{108} = \frac{203}{108}$ .