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04 Apr 2025, 02:58
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Difficulty:
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Question Stats:
76% (01:07) correct
24%
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based on 84
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If \(y^3 = 3\sqrt{3}\), what is the value of \(y^9\)?
(A) \(9\sqrt{3}\)
(B) 27
(C) \(27\sqrt{3}\)
(D) 81
(E) \(81\sqrt{3}\)
(A) \(9\sqrt{3}\)
(B) 27
(C) \(27\sqrt{3}\)
(D) 81
(E) \(81\sqrt{3}\)
08 Apr 2025, 10:41
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3√3 = √27 = √3^3 = y^3
y^9 = y^3 * y^3 * y^3 =
√3^3 * √3^3 * √3^3 = √3^9
since the √ divides the power of 9 by two, you get 3^4.5 or 3^4*√3
3^4 is 81 which leads us to 81√3
another way to approach this is that 3√3 * 3√3 = 9√9 = 27
then 27*3√3 = 81√3
y^9 = y^3 * y^3 * y^3 =
√3^3 * √3^3 * √3^3 = √3^9
since the √ divides the power of 9 by two, you get 3^4.5 or 3^4*√3
3^4 is 81 which leads us to 81√3
another way to approach this is that 3√3 * 3√3 = 9√9 = 27
then 27*3√3 = 81√3
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