Prove: \[ \sqrt{\frac{1}{4}} + (0.01)^{-1/2} – 27^{2/3} = \frac{3}{2} \]
Solution
\[ \sqrt{\frac{1}{4}} = \frac{1}{2} \]
\[ 0.01 = 10^{-2} \]
\[ (0.01)^{-1/2} = (10^{-2})^{-1/2} = 10^1 = 10 \]
\[ 27^{2/3} = (3^3)^{2/3} = 3^2 = 9 \]
\[ = \frac{1}{2} + 10 – 9 \]
\[ = \frac{1}{2} + 1 \]
\[ = \frac{3}{2} \]