Question

Choose the correct word/answer and fill in the blanks:

${\left(-1\right)}^{11}$ and $1^{11}$ are _________ (same/different)

Answer 1

By the properties of exponent, we know that -

$$\begin{gathered} 1^x=1 \\ {a}^x=a\times a\times a\times .........\text{x times} \end{gathered}$$

Whenever negative number is multiplied “odd” number of times, then it always results in negative value.

By using the above property -

$$\begin{gathered} {\left(-1\right)}^{11}=-1\left(11\text{is an odd number}\right) \\ {1}^{11}=1 \end{gathered}$$

Since, ${\left(-1\right)}^{11}$ and $1^{11}$ are not having the same value,

therefore, the correct answer is different.