Question

Which is the value of this expression when m = 3 and n = negative 5?

(6 m Superscript negative 1 Baseline n Superscript 0 Baseline) Superscript negative 3
A. –8
B. Negative StartFraction 1 Over 8 EndFraction
C. one-eighth
D. 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 the values of \(m\) and \(n\)**:
\[
m = 3 \quad \text{and} \quad n = -5
\]
Thus, we replace \(m\) and \(n\) in the expression:
\[
(6 (3)^{-1} (-5)^{0})^{-3}
\]

2. **Evaluate \(n^{0}\)**:
\[
(-5)^{0} = 1 \quad \text{(any non-zero number to the power of 0 is 1)}
\]
Now the expression becomes:
\[
(6 (3)^{-1} (1))^{-3}
\]
This simplifies to:
\[
(6 (3)^{-1})^{-3}
\]

3. **Calculate \(m^{-1}\)**:
\[
(3)^{-1} = \frac{1}{3}
\]
Substitute this back into the expression:
\[
(6 \cdot \frac{1}{3})^{-3}
\]

4. **Simplify inside the parentheses**:
\[
6 \cdot \frac{1}{3} = 2
\]
Now we have:
\[
(2)^{-3}
\]

5. **Evaluate \((2)^{-3}\)**:
\[
(2)^{-3} = \frac{1}{2^3} = \frac{1}{8}
\]

6. **Final expression**:
Therefore, \((6 m^{-1} n^{0})^{-3} = \frac{1}{8}\).

The answer is:
\[
\text{C. one-eighth}
\]