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# Say true or false and justify your answer: ${{2}^{3}}>{{5}^{2}}$

Last updated date: 22nd Mar 2023
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Hint: ${{2}^{3}}$ and ${{5}^{2}}$ are in exponential form. Expand and multiply them.
Compare the value and find if the entity is true or false. Use the basic Exponential formula for the same.

\begin{align} & {{t}^{a}}\times {{t}^{b}}={{t}^{a+b}} \\ & {{\left( {{t}^{a}} \right)}^{b}}={{t}^{a\times b}} \\ \end{align}
If n is a positive integer and x is any real no. , then ${{x}^{n}}$ or simply “x to the n”.
$\therefore {{2}^{3}}=2\times 2\times 2=8$
Similarly ${{5}^{2}}=5\times 5=25$
Given ${{2}^{3}}>{{5}^{2}}$
$\Rightarrow 8>25$, which is wrong.
$\therefore$ The given expression of ${{2}^{3}}>{{5}^{2}}$ is false.
It would be true if ${{2}^{3}}<{{5}^{2}}$.
Note: There are basic rules that exponentiation must follow as well as some band special cases that follow from the rules. In this process, ${{x}^{a}}$for exponents a, that aren’t positive integers, are special cases , or exceptions.