Question

Which exponent rule(s) would be used to simplify this expression? 2x to the fifth power times 12x to the negative fourth power?

Answer 1

To simplify the expression \( 2x^5 \times 12x^{-4} \), you can use the following exponent rules:

1. **Product of Coefficients**: Multiply the numerical coefficients (the numbers in front of the variables).
2. **Product of Powers Rule**: When multiplying like bases, add the exponents.

### Step-by-step simplification:

1. **Multiply the coefficients**:
\[
2 \times 12 = 24
\]

2. **Apply the product of powers rule to the variable \(x\)**:
\[
x^5 \times x^{-4} = x^{5 + (-4)} = x^{5 - 4} = x^1 = x
\]

3. **Combine the results**:
\[
24x
\]

### Final simplified expression:
\[
24x
\]

So, the exponent rules used here are the **Product of Coefficients** and the **Product of Powers Rule**.