To solve the expression [tex]\(\left(2^3\right)^2 + 2^0\)[/tex], we will break it down into smaller parts and then combine the results.
1. Compute [tex]\((2^3)^2\)[/tex]:
- First, calculate [tex]\(2^3\)[/tex].
[tex]\[
2^3 = 2 \times 2 \times 2 = 8
\][/tex]
- Now, raise the result to the power of 2.
[tex]\[
8^2 = 8 \times 8 = 64
\][/tex]
So, [tex]\((2^3)^2 = 64\)[/tex].
2. Compute [tex]\(2^0\)[/tex]:
- By definition of any non-zero number raised to the power of 0:
[tex]\[
2^0 = 1
\][/tex]
3. Add the results from the two parts:
- Now, sum the results of [tex]\((2^3)^2\)[/tex] and [tex]\(2^0\)[/tex].
[tex]\[
64 + 1 = 65
\][/tex]
Therefore, the value of the expression [tex]\(\left(2^3\right)^2 + 2^0\)[/tex] is [tex]\(65\)[/tex].
