Say true or false and justify your answer: ${{2}^{3}}>{{5}^{2}}$
Last updated date: 22nd Mar 2023
•
Total views: 306.6k
•
Views today: 6.86k
Answer
306.6k+ views
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.
Recently Updated Pages
If ab and c are unit vectors then left ab2 right+bc2+ca2 class 12 maths JEE_Main

A rod AB of length 4 units moves horizontally when class 11 maths JEE_Main

Evaluate the value of intlimits0pi cos 3xdx A 0 B 1 class 12 maths JEE_Main

Which of the following is correct 1 nleft S cup T right class 10 maths JEE_Main

What is the area of the triangle with vertices Aleft class 11 maths JEE_Main

The coordinates of the points A and B are a0 and a0 class 11 maths JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
