Sure! Let's solve the given mathematical expression step by step.
The expression we are solving is:
[tex]\[ 5 \cdot \left( \frac{2}{1} + \frac{3}{2} \right)^3 \][/tex]
### Step 1: Evaluate the fractions inside the parentheses
First, we calculate the value of the fractions:
[tex]\[ \frac{2}{1} = 2.0 \][/tex]
[tex]\[ \frac{3}{2} = 1.5 \][/tex]
### Step 2: Sum the evaluated fractions
Now, we add these two values together:
[tex]\[ 2.0 + 1.5 = 3.5 \][/tex]
### Step 3: Raise the sum to the power of 3
Next, we raise the sum to the power of 3:
[tex]\[ 3.5^3 = 42.875 \][/tex]
### Step 4: Multiply by 5
Finally, we multiply the result by 5:
[tex]\[ 5 \cdot 42.875 = 214.375 \][/tex]
### Conclusion
The value of the expression [tex]\( 5 \cdot \left( \frac{2}{1} + \frac{3}{2} \right)^3 \)[/tex] is:
[tex]\[ 214.375 \][/tex]
