(576^1/2+512^1/3)^1/3
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(576^1/2+512^1/3)^1/3
=(√(24*24) + (8³)^(1/3) )^(1/3)
=(24+8)^(1/3)
=32^(1/3)
(Note: check if the question by any chance reads (576^1/2+512^1/3)^1/5)
To evaluate the expression (576^(1/2) + 512^(1/3))^(1/3), we can break it down into three steps:
Step 1: Calculate 576^(1/2)
To calculate the square root of 576, raise it to the power of 1/2:
576^(1/2) = √576 = 24
Step 2: Calculate 512^(1/3)
To calculate the cube root of 512, raise it to the power of 1/3:
512^(1/3) = ∛512 = 8
Step 3: Add the results from step 1 and step 2, and raise the sum to the power of 1/3:
(24 + 8)^(1/3) = 32^(1/3)
The expression can be simplified to 32^(1/3). To evaluate this, we need to calculate the cube root of 32:
32^(1/3) = ∛32 = 2
Therefore, the answer is 2.