Question

Evaluate the expression given below.

3^4 × 3^−3 × (3^−2)^2/3^2 × 3^3 × 3^0


(1 point)
Responses

135
the fraction with numerator 1 and denominator 3 to the 5th power

312
3 to the 12th power

34
3 to the 4th power

138
the fraction with numerator 1 and denominator 3 to the 8th power

Answer 1

To evaluate the expression \(3^4 \times 3^{-3} \times (3^{-2})^2 / 3^2 \times 3^3 \times 3^0\), we can simplify it step-by-step using the laws of exponents.

1. **Simplify the expression:**
- Start by simplifying \((3^{-2})^2\):
\[
(3^{-2})^2 = 3^{-4}
\]
- Substitute back into the expression:
\[
3^4 \times 3^{-3} \times 3^{-4} / 3^2 \times 3^3 \times 3^0
\]

2. **Combine the exponents in the numerator:**
- The numerator is \(3^4 \times 3^{-3} \times 3^{-4}\):
\[
3^{4 - 3 - 4} = 3^{-3}
\]

3. **Combine the exponents in the denominator:**
- The denominator is \(3^2 \times 3^3 \times 3^0\):
\[
3^{2 + 3 + 0} = 3^5
\]

4. **Now, write the entire expression as a single exponent:**
\[
\frac{3^{-3}}{3^5} = 3^{-3 - 5} = 3^{-8}
\]

5. **Rewrite \(3^{-8}\) as a fraction:**
\[
3^{-8} = \frac{1}{3^8}
\]

Now comparing with the provided options, the correct response is:

**the fraction with numerator 1 and denominator 3 to the 8th power.**