27^2/3+1/16^-0,75-25^0,5

To solve the expression \(27^{\frac{2}{3}} + \left(\frac{1}{16}\right)^{-0.75} - 25^{0.5}\), let's break it down step by step: 1. **Calculate \(27^{\frac{2}{3}}\):** The expression \(27^{\frac{2}{3}}\) can be interpreted as the cube root of 27 raised to the power of 2. \[ 27 = 3^3 \] So, the cube root of 27 is 3, and raising this to the power of 2 gives: \[ (27^{\frac{1}{3}})^2 = 3^2 = 9 \] 2. **Calculate \(\left(\frac{1}{16}\right)^{-0.75}\):** The negative exponent means we take the reciprocal of the base and then apply the positive exponent. First, let's express \( \frac{1}{16} \) in terms of a power of 2: \[ \frac{1}{16} = 2^{-4} \] Thus, \( \left(\frac{1}{16}\right)^{-0.75} \) transforms to: \[ (2^{-4})^{-0.75} = 2^{4 \times 0.75} = 2^3 = 8 \] 3. **Calculate \(25^{0.5}\):** The expression \(25^{0.5}\) represents the square root of 25: \[ \sqrt{25} = 5 \] 4. **Combine the results:** Now, you can combine all the computed values: \[ 9 + 8 - 5 = 12 \] Therefore, the value of the expression \(27^{\frac{2}{3}} + \left(\frac{1}{16}\right)^{-0.75} - 25^{0.5}\) is \(12\).