Question

what is the simplification of (-1)4 X (-1)-4​

Answer 1

$\displaystyle \sf{ {( - 1)}^{4} \times {( - 1)}^{ - 4} } = \bf 1$

Correct question :

$\displaystyle \sf what \: is \: the \: simplification \: of \: \: {( - 1)}^{4} \times {( - 1)}^{ - 4}$

Given :

${( - 1)}^{4} \times {( - 1)}^{ - 4}$

To find :

To simplify the expression

Formula :

We are aware of the formula on indices that :

$\sf{1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n} }$

$\displaystyle \sf{2. \: \: {a}^{0} = 1 \: \: for \: a \ne 0}$

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

${( - 1)}^{4} \times {( - 1)}^{ - 4}$

Step 2 of 2 :

Simplify the given expression

${( - 1)}^{4} \times {( - 1)}^{ - 4}$

$\sf = {( - 1)}^{4 + ( - 4)} \: \: \: \bigg[ \: \because \: {a}^{m} \times {a}^{n} = {a}^{m + n}\bigg]$

$\displaystyle \sf{ = {( - 1)}^{(4 - 4)} }$

$\displaystyle \sf{ = {( - 1)}^{0} }$

$\displaystyle \sf{ = 1 }\: \: \: \bigg[ \: \because \: {a}^{0} = 1 \: \: for \: a \ne 0\bigg]$

━━━━━━━━━━━━━━━━

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

#SPJ3