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

How would you simplify the expression (b^-2 / b^-9)?

1. b^7

2. b^1

3. b^-7

4. b^5

The correct answer is: b^7

To simplify the expression \( b^{-2} / b^{-9} \), you can apply the properties of exponents, specifically the quotient of powers rule, which states that when you divide two expressions with the same base, you subtract the exponents. In this case, you have \( b^{-2} \) in the numerator and \( b^{-9} \) in the denominator. Therefore, you can rewrite the expression as: \[ b^{-2 - (-9)} = b^{-2 + 9} \] Calculating the exponent gives: \[ -2 + 9 = 7 \] So, you end up with \( b^7 \). This process demonstrates that the simplification directly follows the rules of exponents, leading to \( b^7 \) as the final simplified form of the expression.