Question

Simplify and express each of the following in exponential form: $\frac{(3\times 7^2\times {11}^8)}{(21\times {11}^3)}$.

Answer 1

Use the appropriate law of exponents

Given: $\frac{(3\times 7^2\times {11}^8)}{(21\times {11}^3)}$

Factors of $21=7\times 3$

The given expression can be written as

$$\begin{gathered} =\frac{(3\times 7^2\times {11}^8)}{(7\times 3\times {11}^3)} \\ =3^{1-1}\times 7^{2-1}\times {11}^{8-3}\left[\because \frac{a^m}{a^n}=a^{m-n}\right] \\ =3^0\times 7\times {11}^5 \\ =1\times 7\times {11}^5 \\ =7\times {11}^5 \end{gathered}$$

Hence, $\frac{(3\times 7^2\times {11}^8)}{(21\times {11}^3)}=7\times {11}^5$