Sure! Let's break down the given expression step by step.
Consider the expression:
[tex]\[ \frac{\frac{6}{4} - \frac{6}{4} \cdot \frac{6}{4}}{\frac{6-2}{4} \cdot \frac{6}{4} \cdot 5 \cdot \frac{6^2}{4}} \][/tex]
First, let's simplify the individual parts.
1. Calculate [tex]\(\frac{6}{4}\)[/tex]:
[tex]\[ \frac{6}{4} = 1.5 \][/tex]
2. Calculate [tex]\(\frac{6}{4} \cdot \frac{6}{4}\)[/tex]:
[tex]\[ 1.5 \cdot 1.5 = 2.25 \][/tex]
3. Calculate the numerator, which is:
[tex]\[ \frac{6}{4} - \frac{6}{4} \cdot \frac{6}{4} \][/tex]
Substitute the values we found:
[tex]\[ 1.5 - 2.25 = -0.75 \][/tex]
Now, let’s move on to the denominator.
4. Calculate [tex]\(\frac{6-2}{4}\)[/tex]:
[tex]\[ \frac{6-2}{4} = \frac{4}{4} = 1.0 \][/tex]
5. Calculate [tex]\(\frac{6}{4}\)[/tex]:
We already know:
[tex]\[ \frac{6}{4} = 1.5 \][/tex]
6. Calculate [tex]\(\frac{6^2}{4}\)[/tex]:
[tex]\[ \frac{6^2}{4} = \frac{36}{4} = 9.0 \][/tex]
7. Now, let's combine these results in the denominator:
[tex]\[ \frac{6-2}{4} \cdot \frac{6}{4} \cdot 5 \cdot \frac{6^2}{4} \][/tex]
Substituting the values:
[tex]\[ 1.0 \cdot 1.5 \cdot 5 \cdot 9.0 \][/tex]
Next, simplify it step by step:
[tex]\[ 1.0 \times 1.5 = 1.5 \][/tex]
[tex]\[ 1.5 \times 5 = 7.5 \][/tex]
[tex]\[ 7.5 \times 9.0 = 67.5 \][/tex]
So, the combined denominator is:
[tex]\[ 67.5 \][/tex]
Now, we combine the simplified numerator and denominator:
[tex]\[ \frac{-0.75}{67.5} = -0.011111111111111112 \][/tex]
Hence, the evaluated expression is:
[tex]\[ \boxed{-0.011111111111111112} \][/tex]
