Question

Question 29

$$\begin{gathered} 20.Express{6}^2\times 7^{-4}\times {\left(8^{-2}\right)}^2\times 6^3\times 7^2\times 8^{4}inthesimplestexponentialform. \\ \left(A\right)6^5{7}^2\left(B\right)\frac{6^5}{7^2} \\ \left(C\right)6^{-5}{7}^2\left(D\right)6^{-5}{7}^{-2} \end{gathered}$$

Answer 1

Dear student

$$\begin{gathered} 6^2\times 7^{-4}\times {\left(8^{-2}\right)}^2\times 6^3\times 7^2\times 8^4 \\ =6^{2+3}\times 7^{-4+2}\times 8^{-4+4}\left[{\left({\mathrm{a}}^{\mathrm{m}}\right)}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{mn}}\mathrm{and}{\mathrm{b}}^{\mathrm{n}}\times {\mathrm{b}}^{\mathrm{c}}={\mathrm{b}}^{\mathrm{n}+\mathrm{c}}\right] \\ =6^5\times 7^{-2}\times 8^0 \\ =\frac{6^5}{7^2}\left[{\mathrm{a}}^0=1\right] \end{gathered}$$
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