Math, asked by kyottabytes, 8 months ago

(-1)×(-1)×(-1)×_____×99 times​

Answers

Answered by DynaMOrtaL
3

Answer:

It's Answer is -1

(-1)×(-1)×(-1)= -1

and, -1 × 99

is -1

Answered by pulakmath007
0

\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: .  \: 99 \: times  } =\bf -1

Given :

The expression

\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: .  \: 99\: 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 . \: . \: .  \: 99\: times  }

Step 2 of 2 :

Simplify the given expression

\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: .  \: 99\: times  }

\displaystyle \sf{ =  {( - 1)}^{99}   }

We know that

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

Now 99 is a odd natural number

Hence we have,

\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: .  \: 99\: times  }

\displaystyle \sf{ =  {( - 1)}^{99}   }

\displaystyle \sf{ = - 1  }

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