Certainly! Let's evaluate the algebraic expression step-by-step.
Sam's steps:
[tex]\[
\sqrt{16 a^{16} + 9 a^{16}}
\][/tex]
[tex]\[
= 4 a^4 + 3 a^4
\][/tex]
[tex]\[
= 7 a^4
\][/tex]
Let's start over and do the calculations step-by-step to check if Sam's work was correct.
1. Combine like terms inside the square root:
[tex]\[
\sqrt{16 a^{16} + 9 a^{16}}
\][/tex]
Combine the terms inside the square root:
[tex]\[
\sqrt{(16 + 9) a^{16}} = \sqrt{25 a^{16}}
\][/tex]
2. Simplify the square root of the combined term:
[tex]\[
\sqrt{25 a^{16}}
\][/tex]
We know that:
[tex]\[
\sqrt{25} = 5 \quad \text{and} \quad \sqrt{a^{16}} = a^{8}
\][/tex]
Therefore:
[tex]\[
\sqrt{25 a^{16}} = 5 a^{8}
\][/tex]
So, the simplified expression is indeed:
[tex]\[
5 a^{8}
\][/tex]
Sam’s solution was incorrect. The correct simplified expression is [tex]\( \boxed{5 a^8} \)[/tex].
