Question

Minus 1 into minus 1 intto minus 10 times is equal to

Answer 1

(-1) × (-1) × (-1) × _ _ _ _ _ _ 10 times is equal to 1

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Answer 2

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: .10 \: times } = 1$

Given :

The expression

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: .10 \: times }$

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

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: .10 \: times }$

Step 2 of 2 :

Simplify the given expression

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: .10 \: times }$

$\displaystyle \sf{ = {( - 1)}^{10} }$

Now we know that

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

Hence we have,

$\displaystyle \sf{( - 1) \times ( - 1) \times . \: . \: . \: .10 \: times }$

$\displaystyle \sf{ = {( - 1)}^{10} }$

$\displaystyle \sf{ = 1 }$

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