Answer:
C
Step-by-step explanation:
Remember that when we have roots (like the square root here), then they can be written as fractional exponents.
Here, we have √2, which is equal to [tex]2^{1/2}[/tex], and we have ∛2, which is equal to [tex]2^{1/3}[/tex]. That means:
(√2)(∛2) = [tex]2^{1/2}*2^{1/3}[/tex]
By property of exponents, when we multiply two exponents with the same base (2 here), we can combine them into one exponent by adding the two powers:
[tex]2^{1/2}*2^{1/3}=2^{1/2+1/3}=2^{3/6+2/6}=2^{5/6}[/tex]
The answer is thus C.
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