Question

Which is the value of this expression when m = 3 and n = negative 5?
pick one
(6 m Superscript negative 1 Baseline n Superscript 0 Baseline) Superscript negative 3
–8
Negative StartFraction 1 Over 8 EndFraction
one-eighth
8

Answer 1

To evaluate the expression \((6 m^{-1} n^{0})^{-3}\) when \(m = 3\) and \(n = -5\), we can follow these steps:

1. **Substitute Values**: Replace \(m\) and \(n\) with their respective values.
\[
= (6 \cdot 3^{-1} \cdot (-5)^{0})^{-3}
\]

2. **Calculate Powers**:
- \(n^{0} = (-5)^{0} = 1\) (any number to the power of 0 is 1)
- \(m^{-1} = 3^{-1} = \frac{1}{3}\)

3. **Substitute Back**:
\[
= (6 \cdot \frac{1}{3} \cdot 1)^{-3}
\]

4. **Simplify Inside the Parentheses**:
\[
= (6 \cdot \frac{1}{3})^{-3} = (2)^{-3}
\]

5. **Evaluate the Negative Power**:
\[
= \frac{1}{2^{3}} = \frac{1}{8}
\]

Thus, the value of the expression is \(\frac{1}{8}\), which can also be written as \(\text{one-eighth}\).

So the correct choice is **one-eighth**.