Question

Which expressions are equivalent to 64 Superscript 1? Check all that apply.
4 cubed
3 Superscript 4
8 squared
2 Superscript 8
6 squared
2 Superscript 6

Answer 1

To determine which expressions are equivalent to \( 64^1 \), we first simplify \( 64^1 \):

\[
64^1 = 64
\]

Next, we can express 64 as a power of 2:

\[
64 = 2^6
\]

Now let's evaluate each of the provided expressions to see which ones equal \( 64 \) or \( 2^6 \):

1. **\( 4^3 \)**:
\[
4^3 = (2^2)^3 = 2^{2 \times 3} = 2^6
\]
This is equal to \( 64 \).

2. **\( 3^4 \)**:
\[
3^4 = 81
\]
This is not equal to \( 64 \).

3. **\( 8^2 \)**:
\[
8^2 = (2^3)^2 = 2^{3 \times 2} = 2^6
\]
This is equal to \( 64 \).

4. **\( 2^8 \)**:
\[
2^8 = 256
\]
This is not equal to \( 64 \).

5. **\( 6^2 \)**:
\[
6^2 = 36
\]
This is not equal to \( 64 \).

6. **\( 2^6 \)**:
\[
2^6 = 64
\]
This is equal to \( 64 \).

Based on this evaluation, the expressions that are equivalent to \( 64^1 \) are:

- \( 4^3 \)
- \( 8^2 \)
- \( 2^6 \)

So the answer is:
**\( 4^3 \), \( 8^2 \), and \( 2^6 \)**.