Question

Which is greater, $2^3\times 2^{4}or{3}^2\times 4^2$ and by how much?

Answer 1

Comparison of exponenets

Given expression: $2^3\times 2^{4}or{3}^2\times 4^2$

We will first solve both and then compare them:

$$\begin{gathered} \Rightarrow 2^3\times 2^4=2^{3+4}[\because x^a\times x^b=x^{a+b}] \\ =2^7 \\ =128 \\ \Rightarrow 3^2\times 4^2=9\times 16 \\ =144 \end{gathered}$$

We can see that $144>128$

Hence, $3^2\times 4^2$ is greater than $2^3\times 2^4$.