Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

When simplifying the expression p^-5 * p^3, what is the correct outcome?

1. p^-2

2. p^2

3. p^{-15}

4. p^15

The correct answer is: p^-2

To simplify the expression \( p^{-5} \times p^{3} \), you can use the property of exponents that states when multiplying terms with the same base, you add their exponents. This is expressed mathematically as follows: \[ p^a \times p^b = p^{a + b} \] In this case, the exponents are -5 and 3. Therefore, you add these exponents together: \[ -5 + 3 = -2 \] This results in: \[ p^{-2} \] The expression \( p^{-2} \) signifies that the exponent is negative, which implies that the term can also be rewritten as \( \frac{1}{p^2} \) if needed. However, since the question only asks for the simplified form, \( p^{-2} \) is already in its simplest exponent format. This makes \( p^{-2} \) the correct outcome for the simplification of the initial expression \( p^{-5} \times p^{3} \).