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

Use (a^m)^n = a^{m·n}.

Compute each:

- (6^0)^16 = 6^{0·16} = 6^0 = 1 → no
- (6^8)^8 = 6^{8·8} = 6^{64} → no
- (6^{-4})^{-4} = 6^{-4·(-4)} = 6^{16} → yes
- (6^{-2})^{-8} = 6^{-2·(-8)} = 6^{16} → yes
- (6^{-1})^{16} = 6^{-1·16} = 6^{-16} → no
- (6^8)^2 = 6^{8·2} = 6^{16} → yes

Equivalent expressions: (6^{-4})^{-4}, (6^{-2})^{-8}, and (6^8)^2.