To solve this problem, we can start by simplifying the exponents.
8^2/3 = (2^3)^2/3 = 2^6/3 = 64^(1/3) = 4
4^3/2 = 2^6/2 = 2^3 = 8
16^-3/4 = (2^4)^-3/4 = 2^-12/4 = 2^-3 = 1/8
Now we can substitute these values back into the expression:
8^2/3 + 4^3/2 ÷ 16^-3/4 = 4 + 8 ÷ (1/8)
Next, we will simplify the division:
8 ÷ (1/8) = 8 * 8 = 64
Finally, we can substitute this value back into the expression:
4 + 64 = 68
Therefore, 8^2/3 + 4^3/2 ÷ 16^-3/4 equals 68.
8^2/3+4^3/2÷16^-3/4
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