Question

-(1)x(-1)X(-1)X .......500 times​

Answer 1

${( - 1)}^{500} = 1$

Hope this will help you...

Answer 2

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: 500 \: times } =\bf 1$

Given :

The expression

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: 500\: times }$

To find :

The value of the expression

Formula :

$\sf {( - 1)}^{n} = \begin{cases} & \sf{ \: \: \: 1\: \: \: \: when \: n \: is \: even} \\ \\ & \sf{ - 1\: \: \: \: \: when \: n \: is \: odd} \end{cases}$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: 500\: times }$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: 500\: times }$

$\displaystyle \sf{ = {( - 1)}^{500} }$

We know that

$\sf {( - 1)}^{n} = \begin{cases} & \sf{ \: \: \: 1\: \: \: \: when \: n \: is \: even} \\ \\ & \sf{ - 1\: \: \: \: \: when \: n \: is \: odd} \end{cases}$

Now 500 is an even natural number

Hence we have,

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: 500\: times }$

$\displaystyle \sf{ = {( - 1)}^{500} }$

$\displaystyle \sf{ = 1 }$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ choose the correct alternative : 100¹⁰⁰ is equal to (a) 2¹⁰⁰ × 50¹⁰⁰ (b) 2¹⁰⁰ + 50¹⁰⁰ (c) 2² × 50⁵⁰ (d) 2² + 50⁵⁰

https://brainly.in/question/47883149

2. Using law of exponents, simplify (5²)³÷5³

https://brainly.in/question/36250730