Question

Choose the correct option and fill in the blanks :

${\left(1^{100}\right)}^2=\_\_\_\_\_\_\_\_.$

Answer 1

Compute the required value:

By the property of exponent, we know that -

${\left(a^x\right)}^y=a^{x\times y}$

By using the above property -

$$\begin{gathered} {\left(1^{100}\right)}^2=1^{100\times 2} \\ =1^{200} \end{gathered}$$

Since, we know that, $1$ is multiplicative identity and multiplying $1$ multiple times results in $1$ only.

Therefore, $1^{200}=1$

Hence, the correct answer is $1$.