Answer:
9
Step-by-step explanation:
I am guessing you´re simplifying this equation.
(The 4 is still an exponent)
Rewrite [tex]\sqrt{-3}[/tex] as [tex]\sqrt{-1(3)}[/tex]
Now rewrite the equation before as [tex](\sqrt{-1} *\sqrt{3} )^{4}[/tex]
Now rewrite [tex]\sqrt{-1}[/tex] as [tex]i[/tex]
[tex](i*\sqrt{3} )^{4}[/tex]
You will then apply the product rule to [tex]i\sqrt{3}[/tex]
[tex]i^{4} \sqrt{3} ^{4}[/tex]
Now rewrite [tex]i^{4}[/tex] as 1
You first have to rewrite
[tex]i^{4} as (i^{2} )^{2} .[/tex]
[tex](i^{2} )^{2} \sqrt{3} ^{4}[/tex]
Now [tex]i^{2} as -1[/tex]
[tex](-1)^{2} \sqrt{3} ^{4}[/tex]
Then raise -1 to the second power
[tex]1\sqrt{3} ^{4}[/tex]
Now multiply [tex]\sqrt{3} ^{4}[/tex] by [tex]1[/tex]
[tex]\sqrt{3} ^{4}[/tex]
Now here comes the longest part
Rewrite [tex]\sqrt{3} ^{4}[/tex] as [tex]3^{2}[/tex]
You first have to use [tex]\sqrt[n]{a^{x} } = a^{\frac{x}{n} }[/tex] to rewrite [tex]\sqrt{3}[/tex] as [tex]3^{\frac{1}{2} }[/tex]
[tex](3^{\frac{1}{2} } )^{4}[/tex]
Apply the power rule and multiply the exponents , [tex](a^{m} )^{n} = a^{mn}[/tex]
[tex]3^{\frac{1}{2} } *4[/tex]
Now combine [tex]\frac{1}{2}[/tex] and [tex]4[/tex]
[tex]3^{\frac{4}{2} }[/tex]
Now you have cancel the common factor of 4 and 2
Factor 2 out of 4
[tex]3^{\frac{2*2}{2} }[/tex]
Cancel the common factors
Now factor 2 out of 2
[tex]3^{\frac{2*2}{2(1)} }[/tex]
Cancel the common factor
[tex]3^{\frac{2*2}{2*1} }[/tex]
Rewrite the expression
[tex]3^{\frac{2}{1} }[/tex]
Divide 2 by 1
[tex]3^{2}[/tex]
Raise 3 to the second power´
9
