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
–8
Negative StartFraction 1 Over 8 EndFraction
one-eighth
8

Answer 1

To evaluate the expression \((6m^{-1} n^{0})^{-3} - 8\) for \(m = 3\) and \(n = -5\), we will follow these steps:

1. **Substitute the values of \(m\) and \(n\)** into the expression:
\[
6m^{-1} n^{0} = 6(3)^{-1} (-5)^{0}
\]

2. **Evaluate \(n^{0}\)**: Any non-zero number raised to the power of 0 is 1, so:
\[
(-5)^{0} = 1
\]

3. **Evaluate \(m^{-1}\)**: This means \(\frac{1}{m}\):
\[
(3)^{-1} = \frac{1}{3}
\]

4. **Insert these values back into the expression**:
\[
6 \left(\frac{1}{3}\right) \cdot 1 = 6 \cdot \frac{1}{3} = 2
\]

5. **Now substitute back into the entire expression**:
\[
(2)^{-3} - 8
\]

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

7. **Now complete the expression including the subtraction**:
\[
\frac{1}{8} - 8
\]

8. **Convert 8 to a fraction** to have a common denominator:
\[
8 = \frac{64}{8}
\]

9. **Now we can perform the subtraction**:
\[
\frac{1}{8} - \frac{64}{8} = \frac{1 - 64}{8} = \frac{-63}{8}
\]

Thus, the final value of the expression is:
\[
\frac{-63}{8}
\]

If we consider the options provided:
1. –8
2. Negative StartFraction 1 Over 8 EndFraction
3. one-eighth
4. 8

None of these match \(\frac{-63}{8}\), so the expression evaluates to \(\frac{-63}{8}\).