Question

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

Answer 1

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.