Question
1. What is the value of the expression below? \[ \frac{3^{2}\left(2^{3}+4\right)}{2^{2}} \]
Ask by Ruiz Love. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
El valor de la expresión es 27.
Solution
Para calcular el valor de la expresión:
\[
\frac{3^{2}\left(2^{3}+4\right)}{2^{2}}
\]
seguimos los siguientes pasos:
1. Calculamos \(3^{2}\):
\[
3^{2} = 9
\]
2. Calculamos \(2^{3}\) y luego sumamos 4:
\[
2^{3} = 8 \\
8 + 4 = 12
\]
3. Multiplicamos los resultados del paso 1 y 2:
\[
9 \times 12 = 108
\]
4. Calculamos \(2^{2}\):
\[
2^{2} = 4
\]
5. Dividimos el numerador entre el denominador:
\[
\frac{108}{4} = 27
\]
**Por lo tanto, el valor de la expresión es 27.**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
Let's break down the expression step by step to find its value. First, calculate inside the parentheses: \[ 2^{3} + 4 = 8 + 4 = 12 \] Next, substitute this back into the expression: \[ \frac{3^{2}(12)}{2^{2}} \] Now calculate \(3^{2}\): \[ 3^{2} = 9 \] So the expression becomes: \[ \frac{9(12)}{2^{2}} \] Now calculate \(2^{2}\): \[ 2^{2} = 4 \] Now substitute this back: \[ \frac{9 \times 12}{4} = \frac{108}{4} \] Finally, divide: \[ 108 \div 4 = 27 \] Therefore, the value of the expression is: \[ \boxed{27} \]
