Question

What is )^4" align="absmiddle" class="latex-formula">

Answer 1

Answer:

9

Step-by-step explanation:

I am guessing you´re simplifying this equation.

(The 4 is still an exponent)

Rewrite $\sqrt{-3}$ as $\sqrt{-1(3)}$

Now rewrite the equation before as $(\sqrt{-1} *\sqrt{3} )^{4}$

Now rewrite $\sqrt{-1}$ as $i$

$(i*\sqrt{3} )^{4}$

You will then apply the product rule to $i\sqrt{3}$

$i^{4} \sqrt{3} ^{4}$

Now rewrite $i^{4}$ as 1

You first have to rewrite

$i^{4} as (i^{2} )^{2} .$

$(i^{2} )^{2} \sqrt{3} ^{4}$

Now $i^{2} as -1$

$(-1)^{2} \sqrt{3} ^{4}$

Then raise -1 to the second power

$1\sqrt{3} ^{4}$

Now multiply $\sqrt{3} ^{4}$ by $1$

$\sqrt{3} ^{4}$

Now here comes the longest part

Rewrite $\sqrt{3} ^{4}$ as $3^{2}$

You first have to use $\sqrt[n]{a^{x} } = a^{\frac{x}{n} }$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2} }$

$(3^{\frac{1}{2} } )^{4}$

Apply the power rule and multiply the exponents , $(a^{m} )^{n} = a^{mn}$

$3^{\frac{1}{2} } *4$

Now combine $\frac{1}{2}$  and $4$

$3^{\frac{4}{2} }$

Now you have cancel the common factor of 4 and 2

Factor 2 out of 4

$3^{\frac{2*2}{2} }$

Cancel the common factors

Now factor 2 out of 2

$3^{\frac{2*2}{2(1)} }$

Cancel the common factor

$3^{\frac{2*2}{2*1} }$

Rewrite the expression

$3^{\frac{2}{1} }$

Divide 2 by 1

$3^{2}$

Raise 3 to the second power´

9

Answer 2

Answer:

9

Step-by-step explanation: