Question
(B) \( \frac{3^{3} 3^{y}+6 \cdot 3^{y-1}}{3^{y}} \)
Ask by Chang Murphy. in South Africa
Feb 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified value of the expression is 29.
Solution
To simplify the expression (3³ · 3^y + 6 · 3^(y–1)) ÷ 3^y, follow these steps:
1. Notice that 3³ · 3^y = 3^(3+y) using the exponent rule a^m · a^n = a^(m+n).
2. Write the expression as:
[3^(y+3) + 6 · 3^(y–1)] ÷ 3^y
3. Divide each term in the numerator by 3^y:
= (3^(y+3) ÷ 3^y) + (6 · 3^(y–1) ÷ 3^y)
4. Simplify each quotient:
• For the first term: 3^(y+3) ÷ 3^y = 3^( (y+3) – y ) = 3³ = 27.
• For the second term: 3^(y–1) ÷ 3^y = 3^( (y–1) – y ) = 3^(–1) = 1/3,
so the term becomes 6 × (1/3) = 2.
5. Add the simplified terms:
27 + 2 = 29.
Thus, the simplified value of the expression is 29.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Beyond the Answer
First, let's simplify the expression step by step. The given expression is: \[ \frac{3^{3} 3^{y} + 6 \cdot 3^{y-1}}{3^{y}} \] We can simplify \(3^3 3^y\) as \(3^{3+y}\). Also, \(6 \cdot 3^{y-1}\) can be rewritten as \(\frac{6}{3} \cdot 3^y = 2 \cdot 3^y\). Now, we rewrite the entire expression: \[ \frac{3^{3+y} + 2 \cdot 3^y}{3^y} \] Next, we can separate the two terms in the numerator: \[ \frac{3^{3+y}}{3^y} + \frac{2 \cdot 3^y}{3^y} \] The first term simplifies to \(3^{3+y-y} = 3^3 = 27\). The second term simplifies to \(2\). Finally, we combine the results: \[ 27 + 2 = 29 \] Thus, the simplified result of the original expression is: \[ 29 \]
