Question

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

[3 marks]
[NCERT-Ex 13.2, Q4(i)]
[Exponential form of numbers]

Answer 1

Solution:
$$\begin{array}{cc}2& 108\\ 2& 54\\ 3& 27\\ 3& 9\\ 3& 3\\ & 1\end{array}$$
[1 mark]

$$\begin{array}{cc}2& 192\\ 2& 96\\ 2& 48\\ 2& 24\\ 2& 12\\ 2& 6\\ 3& 3\\ & 1\end{array}$$
​​​​​​​[1 mark]

$108\times 192$
​​​​​​​$=(2^2\times 3^3)\times (2^6\times 3)$
$=2^{2+6}\times 3^{3+1}$
$=2^8\times 3^4$
[1 mark]