To find the non-permissible value for [tex]\( n \)[/tex] in the expression:
[tex]\[
\frac{-8}{5n}
\][/tex]
we need to determine the value of [tex]\( n \)[/tex] that makes the denominator equal to zero. Division by zero is undefined in mathematics, so the denominator [tex]\( 5n \)[/tex] must not be zero.
Step-by-step solution:
1. Identify the denominator: The denominator of the given expression is [tex]\( 5n \)[/tex].
2. Set the denominator equal to zero and solve for [tex]\( n \)[/tex]:
[tex]\[
5n = 0
\][/tex]
3. Solve the equation:
[tex]\[
n = 0
\][/tex]
Therefore, the non-permissible value for [tex]\( n \)[/tex] is 0. [tex]\( n \)[/tex] cannot be 0 because substituting [tex]\( n = 0 \)[/tex] into the denominator would result in division by zero, which is undefined.
So, the non-permissible replacement for [tex]\( n \)[/tex] in the expression [tex]\( \frac{-8}{5n} \)[/tex] is [tex]\( n = 0 \)[/tex].
