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Sub 505 (Easy)|   Roots|      
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Bunuel
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What is the value of (64^(1/3) + 3^3)/(16)^(1/4) 04 Jun 2021, 08:45
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E
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Difficulty:

5% (low)

Question Stats:

89% (00:43) correct 11% (00:58) wrong based on 111 sessions

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What is the value of \(\frac{\sqrt[3]{64} + 3^3}{(16)^{\frac{1}{4}}}\) ?

A. 17/4

B. 31/4

C. 17/2

D. 35/4

E. 31/2
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E
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What is the value of (64^(1/3) + 3^3)/(16)^(1/4) 04 Jun 2021, 13:41
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=(4+27)/2 =31/2 , Hence E.
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GMAT 2: 760 Q51 V40
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What is the value of (64^(1/3) + 3^3)/(16)^(1/4) 05 Jun 2021, 06:38
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Bunuel
What is the value of \(\frac{\sqrt[3]{64} + 3^3}{(16)^{\frac{1}{4}}}\) ?

A. 17/4

B. 31/4

C. 17/2

D. 35/4

E. 31/2
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Solution:

We simplify the given expression as follows:
      \(\frac{\sqrt[3]{64} + 3^3}{(16)^{\frac{1}{4}}}\)
      = \(\frac{\sqrt[3]{4^3} + 3^3}{(2^4)^{\frac{1}{4}}}\)
      = \(\frac{{4 + 3^3}}{2}\) (since \({\sqrt[n]{a^n}\) = a)
      = \(\frac{{4 + 27}}{2}\)
      = \(\frac{31}{2}\)

Hence, the correct answer is Option E.
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What is the value of (64^(1/3) + 3^3)/(16)^(1/4) 22 Jun 2021, 00:56
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How did you get the denominator as 2?
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Shloka97
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What is the value of (64^(1/3) + 3^3)/(16)^(1/4) 06 Oct 2021, 00:25
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Hi, can someone please explain how the denominator is 2?
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What is the value of (64^(1/3) + 3^3)/(16)^(1/4) 06 Oct 2021, 00:48
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Shloka97
Hi, can someone please explain how the denominator is 2?
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\((16)^{\frac{1}{4}}=\sqrt[4]{16}=\sqrt[4]{2^4}=2\)

8. Exponents and Roots of Numbers



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
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What is the value of (64^(1/3) + 3^3)/(16)^(1/4) 06 Oct 2021, 01:05
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Oh! Thank you so much! For some reason I thought it was 16 x 1/4 and was confused :dazed

Posted from my mobile device
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What is the value of (64^(1/3) + 3^3)/(16)^(1/4) 06 Oct 2021, 02:43
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Bunuel
What is the value of \(\frac{\sqrt[3]{64} + 3^3}{(16)^{\frac{1}{4}}}\) ?

A. 17/4

B. 31/4

C. 17/2

D. 35/4

E. 31/2
Show more
\(\frac{\sqrt[3]{64} + 3^3}{(16)^{\frac{1}{4}}}\)

= \(\frac{\sqrt[3]{4^3} + 3^3}{(2^4)^{\frac{1}{4}}}\)

= \(\frac{{4} + 3^3}{2}\)

= \(\frac{{31}}{2}\), Answer will be (E)
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