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Which of the following equals ?

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sandy
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Which of the following equals ? [#permalink] New post   25 Aug 2018, 14:47
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Which of the following equals \((\sqrt[2]{x})(\sqrt[3]{x})\)?

(A) \(\sqrt[5]{x}\)
(B) \(\sqrt[6]{x}\)
(C) \(\sqrt[3]{x^2}\)
(D) \(\sqrt[5]{x^6}\)
(E) \(\sqrt[6]{x^5}\)
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NickBass
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Re: Which of the following equals ? [#permalink] New post   20 Mar 2020, 02:16
Why is it not (x^1/3)(x^1/2) to get 6th root X?
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Re: Which of the following equals ? [#permalink] New post   18 Jun 2020, 10:01
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sandy wrote:
Which of the following equals \((\sqrt[2]{x})(\sqrt[3]{x})\)?

(A) \(\sqrt[5]{x}\)
(B) \(\sqrt[6]{x}\)
(C) \(\sqrt[3]{x^2}\)
(D) \(\sqrt[5]{x^6}\)
(E) \(\sqrt[6]{x^5}\)



Property #1: \(\sqrt[n]{x} = x^{\frac{1}{n}}\)

Property #2: \(x^{\frac{k}{n}} = (\sqrt[n]{x})^k= \sqrt[n]{x^k}\)


Given: \((\sqrt[2]{x})(\sqrt[3]{x})\)

Apply Property #1 to get: \((x^{\frac{1}{2}})(x^{\frac{1}{3}})\)

Since we're multiplying powers with the same base, we ADD the exponents to get: \(x^{(\frac{1}{2}+\frac{1}{3})}\)

Simplify to get: \(x^{\frac{5}{6}}\)

Apply Property #2 to get: \(\sqrt[6]{x^5}\)

Answer: E

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Re: Which of the following equals ? [#permalink] New post   18 Jun 2020, 10:08
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Re: Which of the following equals ? [#permalink] New post   18 Jun 2020, 10:10
NickBass wrote:
Why is it not (x^1/3)(x^1/2) to get 6th root X?


When we multiply two powers with the same base, we add the exponents (not multiply the exponents)

More here:
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Re: Which of the following equals ? [#permalink] New post   18 Apr 2022, 17:44
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Re: Which of the following equals ? [#permalink]
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