Question

simplify (2⁵/2⁸)⁵* 2^-5

Answer 1

$$\begin{gathered} \mathrm{Consider}\mathrm{the}\mathrm{following}\mathrm{expression}. \\ {\left(\frac{2^5}{2^8}\right)}^5\times 2^{-5} \\ \mathrm{This}\mathrm{can}\mathrm{be}\mathrm{rewritten}\mathrm{as}, \\ ={\left(2^5÷2^8\right)}^5\times 2^{-5} \\ \mathrm{Use}\mathrm{the}\mathrm{formula},{\mathrm{a}}^{\mathrm{n}}÷{\mathrm{a}}^{\mathrm{m}}={\mathrm{a}}^{\mathrm{n}-\mathrm{m}}\mathrm{to}\mathrm{get}, \\ ={\left(2^{5-8}\right)}^5\times 2^{-5} \\ ={\left(2^{-3}\right)}^5\times 2^{-5} \\ ={\left(2\right)}^{-3\times 5}\times 2^{-5}\left(\mathrm{Since}{\left({\mathrm{a}}^{\mathrm{m}}\right)}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{m}\times \mathrm{n}}\right) \\ ={\left(2\right)}^{-15}\times 2^{-5} \\ ={\left(2\right)}^{-15-5}\left(\mathrm{Since}{\mathrm{a}}^{\mathrm{n}}\times {\mathrm{a}}^{\mathrm{m}}={\mathrm{a}}^{\mathrm{n}+\mathrm{m}}\right) \\ ={\left(2\right)}^{-20} \\ =\frac{1}{2^{20}}\left(\mathrm{Since}{\mathrm{a}}^{-\mathrm{n}}=\frac{1}{{\mathrm{a}}^{\mathrm{n}}}\right) \end{gathered}$$