Question

which is the value of this expression when \\(m = 3\\) and \\(n = -5\\)?

\\(6m^{-1}n^0)^{-3}\\

-8

\\(-\frac{1}{8}\\)

\\(\frac{1}{8}\\)

8

Explanation:

Simplify the expression using exponent rules

$$ (6m^{-1}n^0)^{-3} = 6^{-3} \cdot (m^{-1})^{-3} \cdot (n^0)^{-3} = 6^{-3} \cdot m^3 \cdot 1 = \frac{m^3}{6^3} = \frac{m^3}{216} $$

Substitute the given values

$$ \text{Given: } m = 3, \quad n = -5 $$

$$ \frac{3^3}{216} = \frac{27}{216} $$

Simplify the fraction

$$ \frac{27}{216} = \frac{27}{27 \times 8} = \frac{1}{8} $$

Answer:

• -8
• -\(\frac{1}{8}\)
• \(\frac{1}{8}\) (Correct answer)
• 8