Question

Evaluate:

${25}^2\times {(-1)}^{49}$.

Answer 1

Step 1: Find the value of ${25}^2$ and ${(-1)}^{49}$.

Given: ${25}^2\times {(-1)}^{49}$

We know that

$$\begin{gathered} {(-\mathrm{base})}^{\mathrm{odd}\mathrm{number}}=\mathrm{negative}\mathrm{product} \\ {(-\mathrm{base})}^{\mathrm{even}\mathrm{number}}=\mathrm{positive}\mathrm{product} \end{gathered}$$

Now,

In ${25}^2$, Base $=$ $25$ and Power $=$ $2$ i.e., an even number

$\therefore {25}^2=25\times 25=625$

And in ${(-1)}^{49}$,Base $=$ $-1$ and Power $=$ $49$ i.e., an odd number.

$\therefore {(-1)}^{49}=(-1)\times (-1)\times (-1)\times ...\times 49\mathrm{times}=-1$

Step 2: Find the value of ${25}^2\times {(-1)}^{49}$.

${25}^2\times {(-1)}^{49}=625\times (-1)$

$=-625$.

Hence, ${25}^2\times {(-1)}^{49}=-625$.