Question

Which expressions are equivalent to 6 Superscript 16? Check all that apply.
(6 Superscript 0 Baseline) Superscript 16
(6 Superscript 8 Baseline) Superscript 8
(6 Superscript negative 4 Baseline) Superscript negative 4
(6 Superscript negative 2 Baseline) Superscript negative 8
(6 Superscript negative 1 Baseline) Superscript 16
(6 Superscript 8 Baseline) squared

Answer 1

To determine which expressions are equivalent to \( 6^{16} \), let's simplify each option:

1. **\( (6^0)^{16} \)**:
\[
(6^0)^{16} = 1^{16} = 1 \quad \text{(not equivalent)}
\]

2. **\( (6^8)^{8} \)**:
\[
(6^8)^{8} = 6^{8 \times 8} = 6^{64} \quad \text{(not equivalent)}
\]

3. **\( (6^{-4})^{-4} \)**:
\[
(6^{-4})^{-4} = 6^{-4 \times -4} = 6^{16} \quad \text{(equivalent)}
\]

4. **\( (6^{-2})^{-8} \)**:
\[
(6^{-2})^{-8} = 6^{-2 \times -8} = 6^{16} \quad \text{(equivalent)}
\]

5. **\( (6^{-1})^{16} \)**:
\[
(6^{-1})^{16} = 6^{-1 \times 16} = 6^{-16} \quad \text{(not equivalent)}
\]

6. **\( (6^8)^2 \)**:
\[
(6^8)^2 = 6^{8 \times 2} = 6^{16} \quad \text{(equivalent)}
\]

Now, summarizing the results:
- \( (6^{-4})^{-4} \) is equivalent to \( 6^{16} \).
- \( (6^{-2})^{-8} \) is equivalent to \( 6^{16} \).
- \( (6^8)^2 \) is also equivalent to \( 6^{16} \).

Thus, the expressions that are equivalent to \( 6^{16} \) are:
- \( (6^{-4})^{-4} \)
- \( (6^{-2})^{-8} \)
- \( (6^8)^2 \)