Question

Express each of the following as a product of prime factors only in exponential form: $108\times 192$

Answer 1

Factorize the numbers

i)- Factorizing $108\times 192$:

$$\begin{gathered} 108=2\times 2\times 3\times 3\times 3 \\ 108=2^2\times 3^3 \\ 192=2\times 2\times 2\times 2\times 2\times 2\times 3 \\ 192=2^6\times 3 \\ 192\times 108=2^2\times 3^3\times 2^6\times 3\left[a^n\times a^m=a^{n+m}\right] \\ 192\times 108=2^8\times 3^4 \end{gathered}$$

Hence, $192\times 108=2^8\times 3^4$.