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

We know the basic Exponential formula.
\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”.
Here x is the base and n is the exponent or the power.
$\therefore {{2}^{3}}=2\times 2\times 2=8$
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.
Last updated date: 03rd Oct 2023
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