Certainly! Let's go through the solution step-by-step:
1. Calculate the expression within the numerator:
[tex]\[
42 + 8^2 \times 2^2
\][/tex]
- First, we evaluate [tex]\(8^2\)[/tex]:
[tex]\[
8^2 = 64
\][/tex]
- Next, we evaluate [tex]\(2^2\)[/tex]:
[tex]\[
2^2 = 4
\][/tex]
- Now we multiply [tex]\(64\)[/tex] (from [tex]\(8^2\)[/tex]) by [tex]\(4\)[/tex] (from [tex]\(2^2\)[/tex]):
[tex]\[
64 \times 4 = 256
\][/tex]
- Finally, we add [tex]\(42\)[/tex]:
[tex]\[
42 + 256 = 298
\][/tex]
2. Place this result over the denominator:
[tex]\[
\frac{298}{-5}
\][/tex]
3. Calculate the division:
[tex]\[
\frac{298}{-5} = -59.6
\][/tex]
4. Find the cube root of the result:
[tex]\[
\sqrt[3]{-59.6}
\][/tex]
The cube root of a negative number yields a complex number. So let's express it:
[tex]\[
\sqrt[3]{-59.6} \approx (1.9530742653487878 + 3.382823858539359i)
\][/tex]
Therefore, the solution to the expression [tex]\( \sqrt[3]{\frac{42+8^2 \times 2^2}{-5}} \)[/tex] is approximately [tex]\( 1.9530742653487878 + 3.382823858539359i \)[/tex].
