Question

evaluate the expression when x=12/7

1/3(x+9/7)+3^4

Answer 1

To evaluate the expression \( \frac{1}{3}(x + \frac{9}{7}) + 3^4 \) when \( x = \frac{12}{7} \), we will substitute \( x \) with \( \frac{12}{7} \) and simplify the expression step by step.

1. **Substitute \( x \)**:
\[
\frac{1}{3}\left(\frac{12}{7} + \frac{9}{7}\right) + 3^4
\]

2. **Combine the fractions**:
\[
\frac{12}{7} + \frac{9}{7} = \frac{21}{7} = 3
\]

3. **Substitute this back into the expression**:
\[
\frac{1}{3}(3) + 3^4
\]

4. **Simplify \( \frac{1}{3}(3) \)**:
\[
1
\]

5. **Calculate \( 3^4 \)**:
\[
3^4 = 81
\]

6. **Add the results together**:
\[
1 + 81 = 82
\]

So, the value of the expression when \( x = \frac{12}{7} \) is \( \boxed{82} \).