Question

$\sqrt[3]{2} \times \sqrt[4]{2} \times \sqrt[12]{32}$
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Answer 1

Answer:

2^(1/3) * 2 ^ (1/4) * 32 ^ (1/12) = 2

Step-by-step explanation:

2^(1/3) * 2 ^ (1/4) * 32 ^ (1/12)

Lets represent 32 ^ (1/12) with base 2

32 ^ (1/12) = (2^5) ^ (1/12) = 2 ^ (5/12)

Lets multiply all 3 parts since they have the same base

2^(1/3) * 2 ^ (1/4) * 2 ^ (5/12)  = 2 ^ (1/3 + 1/4 + 5/12)  

= 2 ^ (4/12 + 3/12 + 5/12)

= 2 ^ ((4+3+5)/12)

= 2 ^ (12/12)

= 2 ^ (1)

= 2