Solve pi^0-{left(1/2right)}^-1+3sqrt{8}+1-sqrt{2}-2sin(45)+2^-1--1^201+5-3sqrt{27}+-2^2+4/-frac{2{3}}

$${ \pi }^{ 0 } - { \left( \frac{ 1 }{ 2 } \right) }^{ -1 } +3 \sqrt{ 8 } +1- \sqrt{ 2 } -2 \sin ( 45 ) + { 2 }^{ -1 } - { -1 }^{ 201 } +5-3 \sqrt{ 27 } + { -2 }^{ 2 } + \frac{ 4 }{ - \frac{ 2 }{ 3 } }$$

Evaluate

$$4\sqrt{2}+\frac{9}{2}-9\sqrt{3}\approx -5.431603019$$

Solution Steps

Calculate \pi to the power of 0 and get 1.

$$1-\left(\frac{1}{2}\right)^{-1}+3\sqrt{8}+1-\sqrt{2}-2\sin(45)+2^{-1}-\left(-1\right)^{201}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Calculate \frac{1}{2} to the power of -1 and get 2.

$$1-2+3\sqrt{8}+1-\sqrt{2}-2\sin(45)+2^{-1}-\left(-1\right)^{201}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Subtract 2 from 1 to get -1.

$$-1+3\sqrt{8}+1-\sqrt{2}-2\sin(45)+2^{-1}-\left(-1\right)^{201}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Factor 8=2^{2}\times 2. Rewrite the square root of the product \sqrt{2^{2}\times 2} as the product of square roots \sqrt{2^{2}}\sqrt{2}. Take the square root of 2^{2}.

$$-1+3\times 2\sqrt{2}+1-\sqrt{2}-2\sin(45)+2^{-1}-\left(-1\right)^{201}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Multiply 3 and 2 to get 6.

$$-1+6\sqrt{2}+1-\sqrt{2}-2\sin(45)+2^{-1}-\left(-1\right)^{201}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Add -1 and 1 to get 0.

$$6\sqrt{2}-\sqrt{2}-2\sin(45)+2^{-1}-\left(-1\right)^{201}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Combine 6\sqrt{2} and -\sqrt{2} to get 5\sqrt{2}.

$$5\sqrt{2}-2\sin(45)+2^{-1}-\left(-1\right)^{201}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Get the value of \sin(45) from trigonometric values table.

$$5\sqrt{2}-2\times \frac{\sqrt{2}}{2}+2^{-1}-\left(-1\right)^{201}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Cancel out 2 and 2.

$$5\sqrt{2}-\sqrt{2}+2^{-1}-\left(-1\right)^{201}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Combine 5\sqrt{2} and -\sqrt{2} to get 4\sqrt{2}.

$$4\sqrt{2}+2^{-1}-\left(-1\right)^{201}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$4\sqrt{2}+\frac{1}{2}-\left(-1\right)^{201}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Calculate -1 to the power of 201 and get -1.

$$4\sqrt{2}+\frac{1}{2}-\left(-1\right)+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

The opposite of -1 is 1.

$$4\sqrt{2}+\frac{1}{2}+1+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Add \frac{1}{2} and 1 to get \frac{3}{2}.

$$4\sqrt{2}+\frac{3}{2}+5-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Add \frac{3}{2} and 5 to get \frac{13}{2}.

$$4\sqrt{2}+\frac{13}{2}-3\sqrt{27}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Factor 27=3^{2}\times 3. Rewrite the square root of the product \sqrt{3^{2}\times 3} as the product of square roots \sqrt{3^{2}}\sqrt{3}. Take the square root of 3^{2}.

$$4\sqrt{2}+\frac{13}{2}-3\times 3\sqrt{3}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Multiply -3 and 3 to get -9.

$$4\sqrt{2}+\frac{13}{2}-9\sqrt{3}+\left(-2\right)^{2}+\frac{4}{-\frac{2}{3}}$$

Calculate -2 to the power of 2 and get 4.

$$4\sqrt{2}+\frac{13}{2}-9\sqrt{3}+4+\frac{4}{-\frac{2}{3}}$$

Add \frac{13}{2} and 4 to get \frac{21}{2}.

$$4\sqrt{2}+\frac{21}{2}-9\sqrt{3}+\frac{4}{-\frac{2}{3}}$$

Divide 4 by -\frac{2}{3} by multiplying 4 by the reciprocal of -\frac{2}{3}.

$$4\sqrt{2}+\frac{21}{2}-9\sqrt{3}+4\left(-\frac{3}{2}\right)$$

Multiply 4 and -\frac{3}{2} to get -6.

$$4\sqrt{2}+\frac{21}{2}-9\sqrt{3}-6$$

Subtract 6 from \frac{21}{2} to get \frac{9}{2}.

$$4\sqrt{2}+\frac{9}{2}-9\sqrt{3}$$