Question

Choose the correct word/answer and fill in the blanks :

$4^2\times 3$ is ________ than ${\left(4^2\right)}^3.\text{(greater/smaller)}$

Answer 1

Step 1: Simplifying $4^2\times 3$ and ${\left(4^2\right)}^3$ -

$$\begin{gathered} 4^2\times 3=4\times 4\times 3 \\ =48 \end{gathered}$$

and

$$\begin{gathered} {\left(4^2\right)}^3=4^{2\times 3}\left[{\left(a^x\right)}^y=a^{x\times y}\right] \\ =4^6 \\ =4096 \end{gathered}$$

Step 2: Comparing both the values -

$$\begin{gathered} 48<4096 \\ {4}^2\times 3<{\left(4^2\right)}^3 \end{gathered}$$

Hence, $4^2\times 3$ is smaller than ${\left(4^2\right)}^3$.