Question

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

Answer 1

To determine which expressions are equivalent to \(6^{16}\), we can analyze each option based on the rules of exponents.

**Option A:** \((6^{0})^{16}\)
- \(6^{0} = 1\), so \((6^{0})^{16} = 1^{16} = 1\), which is not equivalent to \(6^{16}\).

**Option B:** \((6^{8})^{8}\)
- Using the property of exponents \((a^{m})^{n} = a^{m \cdot n}\):
\[
(6^{8})^{8} = 6^{8 \cdot 8} = 6^{64}
\]
This is not equivalent to \(6^{16}\).

**Option C:** \((6^{-4})^{-4}\)
- Again using the power of a power property:
\[
(6^{-4})^{-4} = 6^{-4 \cdot (-4)} = 6^{16}
\]
This is equivalent to \(6^{16}\).

**Option D:** \((6^{-2})^{-8}\)
- Using the power of a power property:
\[
(6^{-2})^{-8} = 6^{-2 \cdot (-8)} = 6^{16}
\]
This is equivalent to \(6^{16}\).

**Option E:** \((6^{-1})^{16}\)
- Again using the power of a power property:
\[
(6^{-1})^{16} = 6^{-1 \cdot 16} = 6^{-16}
\]
This is not equivalent to \(6^{16}\).

**Option F:** \((6^{8})^{2}\)
- Using the power of a power property:
\[
(6^{8})^{2} = 6^{8 \cdot 2} = 6^{16}
\]
This is equivalent to \(6^{16}\).

Based on the analysis, the equivalent expressions to \(6^{16}\) are:

- **C. (6^{-4})^{-4}**
- **D. (6^{-2})^{-8}**
- **F. (6^{8})^{2}**