To solve the given expression
[tex]\[
\sqrt{a^3 - 7} + |b|
\][/tex]
when [tex]\( a = 2 \)[/tex] and [tex]\( b = -4 \)[/tex], follow these steps:
1. Evaluate [tex]\( a^3 \)[/tex]:
[tex]\[
a = 2 \implies a^3 = 2^3 = 8
\][/tex]
2. Subtract 7 from [tex]\( a^3 \)[/tex]:
[tex]\[
8 - 7 = 1
\][/tex]
3. Take the square root of the result:
[tex]\[
\sqrt{1} = 1
\][/tex]
4. Evaluate the absolute value of [tex]\( b \)[/tex]:
[tex]\[
b = -4 \implies |b| = |-4| = 4
\][/tex]
5. Add the results from steps 3 and 4:
[tex]\[
1 + 4 = 5
\][/tex]
Therefore, the value of the expression is [tex]\( \boxed{5} \)[/tex].
