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. Calculate [tex]\(m^2\)[/tex]:
[tex]\[
m = -5
\][/tex]
[tex]\[
m^2 = (-5)^2 = 25
\][/tex]
2. Calculate [tex]\(n^2\)[/tex]:
[tex]\[
n = 3
\][/tex]
[tex]\[
n^2 = 3^2 = 9
\][/tex]
3. Sum [tex]\(m^2\)[/tex] and [tex]\(n^2\)[/tex]:
[tex]\[
25 + 9 = 34
\][/tex]
4. Calculate the absolute value of the sum:
[tex]\[
\left|34\right| = 34
\][/tex]
Therefore, the value of the expression [tex]\(\left|m^2 + n^2\right|\)[/tex] is [tex]\( \boxed{34} \)[/tex].
