Question
Evaluate:$\sqrt{\frac{1}{4}}+(0.01)^{-\frac{1}{2}}-(27)^{\frac{2}{3}}$
✓
Answer
$ \sqrt{\frac{1}{4}}+(0.01)^{-\frac{1}{2}}-(27)^{\frac{2}{3}}$
$ =\sqrt{\frac{1}{2} \times \frac{1}{2}}+(0.1 \times 0.1)^{-\frac{1}{2}}-(3 \times 3 \times 3)^{\frac{2}{3}}$
$ =\frac{1}{2}+\left[(0.1)^2\right]^{-\frac{1}{2}}-\left(3^2\right)^{\frac{2}{3}}$
$ =\frac{1}{2}+(0.1)^{2 \times\left(-\frac{1}{2}\right)}-3 \times\left(3 \times \frac{2}{3}\right)$
$ =\frac{1}{2}+(0.1)^{-1}-3^2$
$ =\frac{1}{2}+\frac{1}{0.1}-9$
$ =\frac{1}{2}+\frac{10}{1}-9$
$ =\frac{1+20-18}{2}$
$ =\frac{3}{2}$
$ =1 \frac{1}{2}$
$ =\sqrt{\frac{1}{2} \times \frac{1}{2}}+(0.1 \times 0.1)^{-\frac{1}{2}}-(3 \times 3 \times 3)^{\frac{2}{3}}$
$ =\frac{1}{2}+\left[(0.1)^2\right]^{-\frac{1}{2}}-\left(3^2\right)^{\frac{2}{3}}$
$ =\frac{1}{2}+(0.1)^{2 \times\left(-\frac{1}{2}\right)}-3 \times\left(3 \times \frac{2}{3}\right)$
$ =\frac{1}{2}+(0.1)^{-1}-3^2$
$ =\frac{1}{2}+\frac{1}{0.1}-9$
$ =\frac{1}{2}+\frac{10}{1}-9$
$ =\frac{1+20-18}{2}$
$ =\frac{3}{2}$
$ =1 \frac{1}{2}$
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