Question

Which expression is equivalent to (Starttion 4 Superscript five-fourths Baseline time 4 Superscript one-fourth Baseline Over 4 Superscript one-half baseline Endtion) Superscript one-half? RootIndex 16 StartRoot 4 Superscript 5 Baseline EndRoot StartRoot 2 Superscript 5 EndRoot 2 4 Which of the following is equivalent to (16 Superscript two-thirds Baseline) Superscript one-half? 6 8 12 64

a) 2
b) 4
c) 8
d) 16

Answer 1

The simplified expression for (16^two-thirds)^one-half is the cube root of 16 which is 2, corresponding to option b.

Step-by-step explanation:

First, let's simplify the problem step by step. The question is asking for the equivalent of (16two-thirds)one-half. Using exponent rules, when we raise an exponent to another exponent, we multiply the exponents. Thus, we have the following simplification:

(16two-thirds)one-half = 16(2/3) * (1/2)

This multiplication gives us:

161/3, which is the cube root of 16.

Since 24 = 16, we know that 161/3 equals 2 because the cube root of 24 is 2(4/3), which simplifies down to 21. Therefore, the equivalent expression is 2, which corresponds to option b.