To determine which exponential form equals 1024, let's evaluate each option step by step.
1. For option (a) [tex]\(2^{10}\)[/tex]:
[tex]\[
2^{10} = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 1024
\][/tex]
2. For option (b) [tex]\(2^6\)[/tex]:
[tex]\[
2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64
\][/tex]
3. For option (c) [tex]\(16^2\)[/tex]:
[tex]\[
16^2 = 16 \times 16 = 256
\][/tex]
4. For option (d) [tex]\(\frac{1}{8^2}\)[/tex]:
[tex]\[
8^2 = 8 \times 8 = 64 \Rightarrow \frac{1}{8^2} = \frac{1}{64} \approx 0.015625
\][/tex]
Next, we compare each result to find which one equals 1024:
- [tex]\(2^{10} = 1024\)[/tex]
- [tex]\(2^6 = 64\)[/tex]
- [tex]\(16^2 = 256\)[/tex]
- [tex]\(\frac{1}{8^2} = 0.015625\)[/tex]
Among these results, only [tex]\(2^{10}\)[/tex] is equal to 1024.
Therefore, the correct exponential form for 1024 is:
[tex]\[
\boxed{2^{10}}
\][/tex]
