Question

The expression ${(2^{-1}+3^{-1}+4^{-1})}^0$ is equal to ___ .

• A. 0
• B. 1
• C. 2
• D. -1

Answer 1

The correct option is B 1

We know, for any non-zero interger 'a', $a^0=1$.
The given expression is ${(2^{-1}+3^{-1}+4^{-1})}^0$.
If we verify that the base of the given expression is not a zero, then we can immediately conclude that the value of the given expression is 1.
$2^{-1}+3^{-1}+4^{-1}=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}[\because a^{-m}=\frac{1}{a^m},a\ne 0]=\frac{13}{12}\ne 0$
Therefore, ${(2^{-1}+3^{-1}+4^{-1})}^0=(\frac{13}{12}{)}^0=1$


[Note that $a^{-m}$ is positive if 'a' is positive number.
So, the base of the given expression, which is a sum of positive numbers, in no way can be 0.
Hence, the value of the given expression must be 1.
(We need not actually calculate the sum as we did earlier.)]