Question

25 x a5 x 10 + 5 raise to the power 3 x a raise to the power-3.

Answer 1

$$\begin{gathered} \frac{25\times {\mathrm{a}}^5\times 10}{5^3\times {\mathrm{a}}^{-3}} \\ =\frac{5^2\times {\mathrm{a}}^5\times 5\times 2}{5^3\times {\mathrm{a}}^{-3}} \\ =\frac{5^{2+1}\times {\mathrm{a}}^5\times 2}{5^3\times {\mathrm{a}}^{-3}}\left[\mathbf{as}\mathbf{,}\mathbf{}{\mathbf{a}}^{\mathbf{m}}\mathbf{}\mathbf{.}\mathbf{}{\mathbf{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{m}\mathbf{+}\mathbf{n}}\right] \\ =\frac{5^3\times {\mathrm{a}}^5\times 2}{5^3\times {\mathrm{a}}^{-3}} \\ =\frac{5^3}{5^3}\times \frac{{\mathrm{a}}^5}{{\mathrm{a}}^{-3}}\times 2 \\ =5^{3-3}\times {\mathrm{a}}^{5-\left(-3\right)}\times 2\left[\mathbf{as}\mathbf{,}\mathbf{}{\mathbf{a}}^{\mathbf{m}}\mathbf{}\mathbf{÷}\mathbf{}{\mathbf{a}}^{\mathbf{n}}\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{m}\mathbf{-}\mathbf{n}}\right] \\ =5^0\times {\mathrm{a}}^8\times 2 \\ =1\times {\mathrm{a}}^8\times 2\left[\mathbf{as}\mathbf{,}\mathbf{}{\mathbf{a}}^{\mathbf{0}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\right] \\ =2{\mathrm{a}}^8 \end{gathered}$$