To evaluate the given expression [tex]\( \frac{6}{mnp - m - n} \)[/tex] for [tex]\( m = -16 \)[/tex], [tex]\( n = -1 \)[/tex], and [tex]\( p = -1 \)[/tex], let's proceed step-by-step.
1. Substitute the given values into the expression:
[tex]\[
\frac{6}{(-16) \cdot (-1) \cdot (-1) - (-16) - (-1)}
\][/tex]
2. Evaluate the product [tex]\( m \cdot n \cdot p \)[/tex]:
[tex]\[
(-16) \cdot (-1) \cdot (-1) = -16
\][/tex]
3. Substitute this result back into the expression:
[tex]\[
\frac{6}{-16 - (-16) - (-1)}
\][/tex]
4. Simplify the terms in the denominator:
[tex]\[
-16 - (-16) - (-1) = -16 + 16 + 1 = 1
\][/tex]
5. Now, the expression becomes:
[tex]\[
\frac{6}{1}
\][/tex]
6. Simplify the fraction:
[tex]\[
\frac{6}{1} = 6
\][/tex]
So, the simplified value of the expression [tex]\( \frac{6}{mnp - m - n} \)[/tex] for [tex]\( m = -16 \)[/tex], [tex]\( n = -1 \)[/tex], and [tex]\( p = -1 \)[/tex] is:
[tex]\[
6
\][/tex]
