Question

Simplification of ${18}^2$ to its prime factors is .

• A. $2^2\times 3^4$
• B. $2\times 3^2$
• C. $2\times 3$

Answer 1

The correct option is A $2^2\times 3^4$

Given, ${18}^2$
We have to write 18 as product of its prime factor.
$18=2\times 9=2\times 3\times 3=2\times 3^2$
$\therefore {18}^2=(2\times 3^2{)}^2=2^2\times (3^2{)}^2\left[\right(ab{)}^m=a^m\times b^m]=2^2\times 3^4[(a^m{)}^n=a^{m\times n}]$

Hence,
${18}^2=2^2\times 3^4$