Question

when -1 is multiplied by itself 99 times the product is​

Answer 1

Answer:

$\sf \: \underbrace{( - 1) \times ( - 1) \times ( - 1) \times ... \times ( - 1)} = - 1 \\ \tt \: 99 \: times \:$

Step-by-step explanation:

Given expression is

$\sf \: \underbrace{( - 1) \times ( - 1) \times ( - 1) \times ... \times ( - 1)} \\ \tt \: 99 \: times$

can be rewritten as

$\sf \: = \: \underbrace{( - 1) \times ( - 1) \times ( - 1) \times ... \times ( - 1)} \times ( - 1) \\ \tt \: 98 \: times$

$\sf \: = \: {( - 1)}^{98} \times ( - 1)$

$\sf \: = \: {( - 1)}^{2 \times 49} \times ( - 1)$

$\sf \: = \: {( { (- 1)}^{2} )}^{49} \times ( - 1)$

$\sf \: = \: {( 1 )}^{49} \times ( - 1)$

$\sf \: = \: 1 \times ( - 1)$

$\sf \: = \: - 1$

Hence,

$\implies\sf \: \sf \: \underbrace{( - 1) \times ( - 1) \times ( - 1) \times ... \times ( - 1)} = - 1 \\ \tt \: 99 \: times \:$

$\rule{190pt}{2pt}$

Additional Information

$\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}$

Answer 2

Step-by-step explanation:

Hope this helps you!!!!!