Question

Which is greater?

${\left(7\right)}^{3}or{\left(3\right)}^7$

Answer 1

Hint: ${\left(a\right)}^n=a\times a\times a\times a\times a.....uptonterms$

Step 1: Given expression: ${\left(7\right)}^{3}or{\left(3\right)}^7$

Step2: Solution:

According to given criteria above:

$$\begin{gathered} {\left(3\right)}^7=3\times 3\times 3\times 3\times 3\times 3\times 3 \\ =2187 \\ {\left(7\right)}^3=7\times 7\times 7 \\ =343 \end{gathered}$$

We can see that $2187>343$

Hence ${\left(3\right)}^7$ is greater than ${\left(7\right)}^3$