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

What is the result of (b^-2/b^-9)?

1. b^-11

2. b^7

3. b^7 + 7

4. b^11

The correct answer is: b^7

To find the result of \( \frac{b^{-2}}{b^{-9}} \), we can apply the laws of exponents, specifically the quotient of powers rule, which states that when dividing two expressions with the same base, you subtract the exponent of the denominator from the exponent of the numerator. In this case, the base is \( b \), and the exponents are \(-2\) in the numerator and \(-9\) in the denominator. So, we perform the subtraction: \[ \frac{b^{-2}}{b^{-9}} = b^{-2 - (-9)} = b^{-2 + 9} = b^{7} \] The result is \( b^7 \). This is why the correct answer is \( b^7 \), as it accurately reflects the application of the exponent rules to simplify the expression. The other choices either misapply the laws of exponents or introduce incorrect manipulation of the expression, which is why they do not yield the correct result.