Solve E=sqrt{27^{-3^{-1}}+36^-2^-1+(4/3)^-1-2^-2}quadE=

$$E = \sqrt { 27 ^ { - 3 ^ { - 1 } } + 36 ^ { - 2 ^ { - 1 } } + ( \frac { 4 } { 3 } ) ^ { - 1 } - 2 ^ { - 2 } } \quad E =$$

Solve for E (complex solution)

$$E\in \mathrm{C}$$

Solution Steps

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$E=\sqrt{27^{-\frac{1}{3}}+36^{-2^{-1}}+\left(\frac{4}{3}\right)^{-1}-2^{-2}}E$$

Calculate 27 to the power of -\frac{1}{3} and get \frac{1}{3}.

$$E=\sqrt{\frac{1}{3}+36^{-2^{-1}}+\left(\frac{4}{3}\right)^{-1}-2^{-2}}E$$

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

$$E=\sqrt{\frac{1}{3}+36^{-\frac{1}{2}}+\left(\frac{4}{3}\right)^{-1}-2^{-2}}E$$

Calculate 36 to the power of -\frac{1}{2} and get \frac{1}{6}.

$$E=\sqrt{\frac{1}{3}+\frac{1}{6}+\left(\frac{4}{3}\right)^{-1}-2^{-2}}E$$

Add \frac{1}{3} and \frac{1}{6} to get \frac{1}{2}.

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

Calculate \frac{4}{3} to the power of -1 and get \frac{3}{4}.

$$E=\sqrt{\frac{1}{2}+\frac{3}{4}-2^{-2}}E$$

Add \frac{1}{2} and \frac{3}{4} to get \frac{5}{4}.

$$E=\sqrt{\frac{5}{4}-2^{-2}}E$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$E=\sqrt{\frac{5}{4}-\frac{1}{4}}E$$

Subtract \frac{1}{4} from \frac{5}{4} to get 1.

$$E=\sqrt{1}E$$

Calculate the square root of 1 and get 1.

$$E=1E$$

Subtract 1E from both sides.

$$E-E=0$$

Combine E and -E to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any E.

$$E\in \mathrm{C}$$

Solve for E

$$E\in \mathrm{R}$$

Solution Steps

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$E=\sqrt{27^{-\frac{1}{3}}+36^{-2^{-1}}+\left(\frac{4}{3}\right)^{-1}-2^{-2}}E$$

Calculate 27 to the power of -\frac{1}{3} and get \frac{1}{3}.

$$E=\sqrt{\frac{1}{3}+36^{-2^{-1}}+\left(\frac{4}{3}\right)^{-1}-2^{-2}}E$$

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

$$E=\sqrt{\frac{1}{3}+36^{-\frac{1}{2}}+\left(\frac{4}{3}\right)^{-1}-2^{-2}}E$$

Calculate 36 to the power of -\frac{1}{2} and get \frac{1}{6}.

$$E=\sqrt{\frac{1}{3}+\frac{1}{6}+\left(\frac{4}{3}\right)^{-1}-2^{-2}}E$$

Add \frac{1}{3} and \frac{1}{6} to get \frac{1}{2}.

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

Calculate \frac{4}{3} to the power of -1 and get \frac{3}{4}.

$$E=\sqrt{\frac{1}{2}+\frac{3}{4}-2^{-2}}E$$

Add \frac{1}{2} and \frac{3}{4} to get \frac{5}{4}.

$$E=\sqrt{\frac{5}{4}-2^{-2}}E$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$E=\sqrt{\frac{5}{4}-\frac{1}{4}}E$$

Subtract \frac{1}{4} from \frac{5}{4} to get 1.

$$E=\sqrt{1}E$$

Calculate the square root of 1 and get 1.

$$E=1E$$

Subtract 1E from both sides.

$$E-E=0$$

Combine E and -E to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any E.

$$E\in \mathrm{R}$$