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

Last updated date: 22nd Mar 2023

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Answer

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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.

Complete step-by-step answer:

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.

Compare the value and find if the entity is true or false. Use the basic Exponential formula for the same.

Complete step-by-step answer:

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.

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