Question

Simplify
(i) (4³)⁴*(2³)⁴*(8/15)-2
(ii) 8² -4*4⁰-(1/4)^-2

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right). \\ {\left(4^3\right)}^4\times {\left(2^3\right)}^4\times {\left(\frac{8}{15}\right)}^{-2} \\ =4^{12}\times 2^{12}\times {\left(\frac{15}{8}\right)}^2\left[\mathbf{as}\mathbf{,}\mathbf{}{\left({\mathbf{a}}^{\mathbf{m}}\right)}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{mn}}\mathbf{}\mathbf{and}\mathbf{}{\mathbf{a}}^{\mathbf{-}\mathbf{m}}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{1}}{{\mathbf{a}}^{\mathbf{m}}}\right] \\ ={\left(2^2\right)}^{12}\times 2^{12}\times {\left[\frac{15}{2^3}\right]}^2 \\ =2^{24}\times 2^{12}\times \frac{{15}^2}{2^6} \\ =\frac{2^{24}\times 2^{12}}{2^6}\times {15}^2 \\ =\frac{2^{36}}{2^6}\times 225\left[\mathbf{as}\mathbf{,}\mathbf{}{\mathbf{a}}^{\mathbf{m}}\mathbf{}\mathbf{.}\mathbf{}{\mathbf{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{m}\mathbf{+}\mathbf{n}}\right] \\ =2^{36-6}\times 225\mathbf{}\left[\mathbf{as}\mathbf{,}\mathbf{}{\mathbf{a}}^{\mathbf{m}}\mathbf{}\mathbf{÷}\mathbf{}{\mathbf{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{m}\mathbf{-}\mathbf{n}}\right] \\ =2^{30}\times 225 \end{gathered}$$