Prove $2^0 =1$.
To do:
We have to prove that $2^0 =1$.
Solution:
We know that,
$\frac{a^m}{a^n}=a^{m-n}$
$2^0$ can be written as $2^{1-1}$ .
$2^{1-1}=\frac{2^1}{2^1}$
$=\frac{2}{2}$
$=1$
Hence proved.
Related Articles
- Prove that the point $(-2, 5), (0, 1)$ and $(2, -3)$ are collinear.
- Prove that:\( 9^{\frac{3}{2}}-3 \times 5^{0}-\left(\frac{1}{81}\right)^{\frac{-1}{2}}=15 \)
- If the equation $(1+m^2)x^2+2mcx+(c^2-a^2)=0$ has equal roots, prove that $c^2=a^2(1+m^2)$.
- Prove that the points $(a, 0), (0, b)$ and $(1, 1)$ are collinear if, $\frac{1}{a} + \frac{1}{b} = 1$.
- Following data gives the number of children in 41 families:$1, 2, 6, 5, 1, 5, 1, 3, 2, 6, 2, 3, 4, 2, 0, 0, 4, 4, 3, 2, 2, 0, 0, 1, 2, 2, 4, 3, 2, 1, 0, 5, 1, 2, 4, 3, 4, 1, 6, 2, 2.$Represent it in the form of a frequency distribution.
- Three coins were tossed 30 times. Each time the number of heads occuring was noted down as follow:0 1 2 2 1 2 3 1 3 01 3 1 1 2 2 0 1 2 13 0 0 1 1 2 3 2 2 0Prepare a frequency distribution table for the data given above.
- Prove that the points $(-4, -1), (-2, -4), (4, 0)$ and $(2, 3)$ are the vertices of a rectangle.
- If $a ≠ b ≠ 0$, prove that the points $(a, a^2), (b, b^2), (0, 0)$ are never collinear.
- Prove that:\( \frac{(0.6)^{0}-(0.1)^{-1}}{\left(\frac{3}{8}\right)^{-1}\left(\frac{3}{2}\right)^{3}+\left(-\frac{1}{3}\right)^{-1}}=-\frac{3}{2} \)
- Prove that:\( \frac{2^{n}+2^{n-1}}{2^{n+1}-2^{n}}=\frac{3}{2} \)
- Factorize $35x^2+12x+1=0$.
- Prove the following trigonometric identities:\( \cos ^{2} A+\frac{1}{1+\cot ^{2} A}=1 \)
- Prove the following trigonometric identities:\( \sin ^{2} A+\frac{1}{1+\tan ^{2} A}=1 \)
- Prove that \( \frac{a^{-1}}{a^{-1}+b^{-1}}+\frac{a^{-1}}{a^{-1}-b^{-1}}=\frac{2 b^{2}}{b^{2}-a^{2}} \)
- Prove that:\( \frac{\tan ^{2} A}{1+\tan ^{2} A}+\frac{\cot ^{2} A}{1+\cot ^{2} A}=1 \)
Kickstart Your Career
Get certified by completing the course
Get Started
Data Structure
Networking
RDBMS
Operating System
Java
MS Excel
iOS
HTML
CSS
Android
Python
C Programming
C++
C#
MongoDB
MySQL
Javascript
PHP
Physics
Chemistry
Biology
Mathematics
English
Economics
Psychology
Social Studies
Fashion Studies
Legal Studies