To demonstrate that Steven's claim is incorrect, we need to consider the rule for multiplying powers with the same base. The correct rule states that when you multiply two powers with the same base, you add the exponents, not multiply them.
For example, if we use \( 3^2 \) and \( 3^3 \):
According to the correct rule: \[ 3^2 \times 3^3 = 3^{(2 + 3)} = 3^5 \]
If we were to follow Steven's incorrect claim and multiply the exponents: \[ 3^2 \times 3^3 = 3^{(2 \times 3)} = 3^6 \]
Thus, to create an equation that shows Steven's claim is incorrect, we can set up:
- Take the bases: \(3\)
- Choose exponents: \(2\) and \(3\)
The equation: \[ 3^2 \times 3^3 = 3^6 \quad (\text{Steven's claim}) \] \[ 3^2 \times 3^3 = 3^5 \quad (\text{Correct exponent addition}) \]
So, filling in the boxes into the equation from the example:
- First box (exponent): 2
- Second box (exponent): 3
You can use: \[ 3^2 \times 3^3 = 3^{(2 \times 3)} \text{ (Steven's incorrect claim)} \]
This example clearly shows that \( 3^2 \times 3^3 = 3^6 \) is not equal to \( 3^5 \), thus demonstrating Steven's claim is incorrect.