Question

which expression is equivalent to 3^3 *3
9^10/3^10
1/3^10
3^9
1/3^9

Answer 1

To determine which expression is equivalent to \( 3^3 \cdot 3 \), let’s simplify it first:

\[
3^3 \cdot 3 = 3^3 \cdot 3^1 = 3^{3+1} = 3^4
\]

Now, let's analyze the other given expressions to see if any of them are equivalent to \( 3^4 \).

1. **9^10 / 3^10**:
\[
9^{10} = (3^2)^{10} = 3^{20}
\]
Therefore:
\[
\frac{9^{10}}{3^{10}} = \frac{3^{20}}{3^{10}} = 3^{20 - 10} = 3^{10}
\]

2. **1/3^{10}**:
This expression does not equal \( 3^4 \) and is simply \( 3^{-10} \).

3. **3^9**:
This is simply \( 3^9 \), which is not equal to \( 3^4 \).

4. **1/3^9**:
This expression is \( 3^{-9} \), which is also not equal to \( 3^4 \).

Now, none of the following expressions equal \( 3^4 \) based on the above calculations. Therefore, we conclude that none of the given expressions are equivalent to \( 3^3 \cdot 3 \).

To summarize, the equivalent of \( 3^3 \cdot 3 \) is \( 3^4 \), and none of the options provided are equal to \( 3^4 \).