To find the value of the expression [tex]\(\left|m^2 + n^2\right|\)[/tex] when [tex]\(m = -5\)[/tex] and [tex]\(n = 3\)[/tex], follow these steps:
1. Square the value of [tex]\(m\)[/tex]:
[tex]\[
m^2 = (-5)^2 = 25
\][/tex]
2. Square the value of [tex]\(n\)[/tex]:
[tex]\[
n^2 = 3^2 = 9
\][/tex]
3. Add the squared values:
[tex]\[
m^2 + n^2 = 25 + 9 = 34
\][/tex]
4. Take the absolute value of the result:
[tex]\[
\left|34\right| = 34
\][/tex]
Therefore, the value of the expression [tex]\(\left|m^2 + n^2\right|\)[/tex] when [tex]\(m = -5\)[/tex] and [tex]\(n = 3\)[/tex] is [tex]\(34\)[/tex].
So, [tex]\(\boxed{34}\)[/tex]
