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

For the expression (1/6m^-2), how do you simplify it?

1. (m^2/6)

2. (1/(6m^2))

3. (1/6m)

4. (6/m^2)

The correct answer is: (m^2/6)

To simplify the expression \( \frac{1}{6m^{-2}} \), it's important to understand how negative exponents work. The negative exponent indicates that the base should be moved to the opposite position in the fraction. Specifically, \( m^{-2} \) can be rewritten as \( \frac{1}{m^2} \). So, we can transform the original expression: \[ \frac{1}{6m^{-2}} = \frac{1}{6 \cdot \frac{1}{m^2}} = \frac{m^2}{6} \] This shows that when you simplify \( \frac{1}{6m^{-2}} \), you end up with \( \frac{m^2}{6} \). Therefore, the correct choice is \( \frac{m^2}{6} \), which matches the initial answer given. The simplification relies on understanding the rule for negative exponents, which clarifies why the final result takes the form of \( \frac{m^2}{6} \).