Question

9^3/2 +27^2/3 - (1/16)^3/4

Answer 1

$9^{\frac{3}{2} }+27^{\frac{2}{3} }-(\frac{1}{16})^{\frac{3}{4} }=(3^{2})^{\frac{3}{2} }+(3^{3})^{\frac{2}{3} }-((\frac{1}{2})^{4})^{\frac{3}{4}}=3^{3}+3^{2}-(\frac{1}{2})^{3}=27+9-0,125=35,875$

Answer 2

Let's break down the expression step by step:

1. First, we'll evaluate 9^(3/2): 9^(3/2) = (sqrt(9))^3 = 3^3 = 27

2. Next, we'll evaluate 27^(2/3): 27^(2/3) = (cbrt(27))^2 = 3^2 = 9

3. Finally, we'll evaluate (1/16)^(3/4): (1/16)^(3/4) = (1/2^4)^(3/4) = 1/2^3 = 1/8

Now we can substitute these values back into the original expression:

9^(3/2) + 27^(2/3) - (1/16)^(3/4) = 27 + 9 - 1/8 = 36 - 1/8 = 287/8

Therefore, the final answer is 287/8.