Question

8. Find the value of the expression:
(ii) (27)^4/3 - 2 * (16)^5/4 + 1/3 * 9^3/2 + (9^-1/2)^-1

Answer 1

$$\begin{gathered} \mathrm{Dear}\mathrm{Student}, \\ {\left(27\right)}^{\frac{4}{3}}-2{\left(16\right)}^{\frac{5}{4}}+\frac{1}{3}\times 9^{\frac{3}{2}}+{\left[{\left(9\right)}^{-\frac{1}{2}}\right]}^{-1} \\ ={\left(3^3\right)}^{\frac{4}{3}}-2{\left(2^4\right)}^{\frac{5}{4}}+3^{-1}\times {\left(3^2\right)}^{\frac{3}{2}}+{\left[{\left(3^2\right)}^{-\frac{1}{2}}\right]}^{-1} \\ =3^{3\times \frac{4}{3}}-2\times 2^{4\times \frac{5}{4}}+3^{-1}\times \left(3^{2\times \frac{3}{2}}\right)+{\left[\left(3^{2\times -\frac{1}{2}}\right)\right]}^{-1} \\ =3^4-2\times 2^5+3^{-1}\times 3^3+3^{-1\times -1} \\ =81-64+9+3 \\ =29 \\ \mathrm{Regards} \end{gathered}$$