Question

If $S=1^0+2^0+3^0+4^0+\dots +{50}^0,$ then the value of $S$ is

• A. $0$
• B. $1^{50}$
• C. $50$
• D. $100$

Answer 1

The correct option is C $50$

$S=1^0+2^0+3^0+4^0+\dots +{50}^0$
Since, we know that
$\frac{a^m}{a^n}=a^{m-n}$
When $m=n$, then
$\frac{a^m}{a^m}=a^{m-m}=a^0=1$, where $a$ is any real number except 0.
Hence, we get that
$1^0=1$
$2^0=1$
$3^0=1$
$⋮$
${50}^0=1$

$\therefore S=1+1+1+\dots +1\left(50\text{times}\right)$
$\Rightarrow S=1\times 50$
$\Rightarrow S=50$