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Q10 Choose all of the expressions that are equivalent to 6^1/8.
(36^5/16)(6^−1/2)
(6^5/8)(6^−12)
6(6^7/8)
^8√6^5
^8√6^5
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GPT-5 mini
AI
Correct choices: the first and second expressions.
Work:
- (36^{5/16})(6^{-1/2}) = (6^2)^{5/16}·6^{-1/2} = 6^{10/16}·6^{-4/8} = 6^{5/8}·6^{-4/8} = 6^{1/8}.
- (6^{5/8})(6^{-1/2}) = 6^{5/8 - 4/8} = 6^{1/8}.
The others are not equal:
- 6·6^{7/8} = 6^{15/8}.
- ^8√(6^5) = (6^5)^{1/8} = 6^{5/8} (appears twice).
Work:
- (36^{5/16})(6^{-1/2}) = (6^2)^{5/16}·6^{-1/2} = 6^{10/16}·6^{-4/8} = 6^{5/8}·6^{-4/8} = 6^{1/8}.
- (6^{5/8})(6^{-1/2}) = 6^{5/8 - 4/8} = 6^{1/8}.
The others are not equal:
- 6·6^{7/8} = 6^{15/8}.
- ^8√(6^5) = (6^5)^{1/8} = 6^{5/8} (appears twice).
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