Question

Which one is greater?

${\left(3^2\right)}^4$ or $\left(3^2\right)\times 4$

Answer 1

I] ${\left(3^2\right)}^4$ is of the form ${\left(a^m\right)}^n$

Here, $a=3,m=2,n=4$

So, ${\left(a^m\right)}^n$$=a^{m\times n}$

then ${\left(3^2\right)}^4$$=3^{2\times 4}$

$=3^8$.

Now, $3^8$$=3\times 3\times 3\times 3\times 3\times 3\times 3\times 3$ ($3$ is multiplied $8$ times)

$=6561$.

Hence, ${\left(3^2\right)}^4$$=6561$ ……………………$\left(1\right)$

II] $\left(3^2\right)\times 4$ $=$ $3\times 3\times 4$ (As, $3^2$ means we have to multiply the integer $3$ two times)

$=36$.

Hence, $\left(3^2\right)\times 4$$=36$ ……………………$\left(2\right)$

From $\left(1\right)\mathrm{and}\left(2\right)$,

$6561>36$

Therefore, ${\left(3^2\right)}^4$$>$$\left(3^2\right)\times 4$