The product will be 40 I believe?
In the division rule you subtract the exponents<span> when </span>dividing<span> numbers with the same base. </span>One<span> rule for exponents is that exponents add when you have the same base. This works for any number x that you want to plug in except for x = </span>0<span>,because </span>0/0<span> is indeterminate (it is like dividing </span>zero<span> by </span>zero<span>). No matter what number we use when it is raised to the </span>zero power<span> it will always be </span>1.
Answer:
C. Make solving a word problem easier.
Step-by-step explanation:
(√3 - <em>i </em>) / (√3 + <em>i</em> ) × (√3 - <em>i</em> ) / (√3 - <em>i</em> ) = (√3 - <em>i</em> )² / ((√3)² - <em>i</em> ²)
… = ((√3)² - 2√3 <em>i</em> + <em>i</em> ²) / (3 - <em>i</em> ²)
… = (3 - 2√3 <em>i</em> - 1) / (3 - (-1))
… = (2 - 2√3 <em>i</em> ) / 4
… = 1/2 - √3/2 <em>i</em>
… = √((1/2)² + (-√3/2)²) exp(<em>i</em> arctan((-√3/2)/(1/2))
… = exp(<em>i</em> arctan(-√3))
… = exp(-<em>i</em> arctan(√3))
… = exp(-<em>iπ</em>/3)
By DeMoivre's theorem,
[(√3 - <em>i </em>) / (√3 + <em>i</em> )]⁶ = exp(-6<em>iπ</em>/3) = exp(-2<em>iπ</em>) = 1
