Certainly! To solve the expression [tex]\(\sqrt[3]{\left[\frac{38.32 \times 2.964}{8.637 \times 6.285}\right]^2}\)[/tex], let's break it down step by step:
### Step 1: Calculate the Numerator
First, we need to multiply the two numbers in the numerator:
[tex]\[ 38.32 \times 2.964 \][/tex]
This gives us:
[tex]\[ 38.32 \times 2.964 = 113.58048 \][/tex]
### Step 2: Calculate the Denominator
Next, we need to multiply the two numbers in the denominator:
[tex]\[ 8.637 \times 6.285 \][/tex]
This gives us:
[tex]\[ 8.637 \times 6.285 = 54.283545 \][/tex]
### Step 3: Form the Fraction
Now, we form the fraction by dividing the numerator by the denominator:
[tex]\[ \frac{113.58048}{54.283545} \][/tex]
This gives us:
[tex]\[ \frac{113.58048}{54.283545} = 2.0923556116314805 \][/tex]
### Step 4: Square the Fraction
We then square the fraction:
[tex]\[ \left(2.0923556116314805\right)^2 \][/tex]
This gives us:
[tex]\[ \left(2.0923556116314805\right)^2 = 4.377952005525747 \][/tex]
### Step 5: Calculate the Cube Root
Finally, we take the cube root of the squared fraction:
[tex]\[ \sqrt[3]{4.377952005525747} \][/tex]
This gives us:
[tex]\[ \sqrt[3]{4.377952005525747} = 1.635900927849107 \][/tex]
By following these steps, we find that the value of the given expression is approximately [tex]\(1.635900927849107\)[/tex].
