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Say true or false and justify your answer:${2^3} \times {3^2} = {6^5}$

Answer Verified
Hint – In order to do the verification of the given expression, simply write ${2^3}{\text{ as 2}} \times {\text{2}} \times {\text{2}}$ and ${3^2} = 3 \times 3$ in the left hand side, then simplify the right hand side to write ${6^5}$ as ${6^5} = 6 \times 6 \times 6 \times 6 \times 6$. Then check if the simplification part of the left hand side is equal to the right hand side, if yes then the answer is true.

Complete step-by-step answer:
Given expression
${2^3} \times {3^2} = {6^5}$
Consider L.H.S of the above expression
$\Rightarrow {2^3} \times {3^2}$
As we know that $\left( {2 \times 3 = 6} \right)$
$\Rightarrow {2^3} \times {3^2} = 2 \times \left( {2 \times 3} \right) \times \left( {2 \times 3} \right) = 2 \times \left( 6 \right) \times \left( 6 \right)$
$\Rightarrow {2^3} \times {3^2} = 2 \times \left( {{6^2}} \right)$
So as we see that above simplified expression is not equal to the R.H.S of the given statement.
$\Rightarrow {2^3} \times {3^2} \ne {6^5}$
Hence the given statement is false.
So this is the required answer.

Note – In this question we could have used another way to solve this problem, instead of simply considering the L.H.S part and the R.H.S part separately, we could have manipulated the entire equation by taking ${3^2}$ or ${2^3}$ to the right hand side and then simplifying the equation this too will give the right answer.