Question

Put > or < sign in the boxes:

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

Answer 1

Step 1: Given exponential form: ${\left(3\right)}^2\times {\left(4\right)}^2$ and ${\left(2\right)}^3\times {\left(2\right)}^4$

Step2: Solution:

We will solve both exponential forms one by one:

.$$\begin{gathered} {\left(3\right)}^2\times {\left(4\right)}^2=9\times 16 \\ =144 \end{gathered}$$

And $$\begin{gathered} {\left(2\right)}^3\times {\left(2\right)}^4=8\times 16 \\ =128 \end{gathered}$$

Now we can see that $144>128$

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

Final Answer: Hence ${\left(3\right)}^2\times {\left(4\right)}^2>{\left(2\right)}^3\times {\left(2\right)}^4$