Solve 20/4^{2}+[(2/3)^{4}]^{6}:[(2/3)^{11}]^2+(1/3)^16:[(frac{1}{3})^7]^2-frac{5}{4}=

$$\frac { 20 } { 4 ^ { 2 } } + [ ( \frac { 2 } { 3 } ) ^ { 4 } ] ^ { 6 } : [ ( \frac { 2 } { 3 } ) ^ { 11 } ] ^ { 2 } + ( \frac { 1 } { 3 } ) ^ { 16 } : [ ( \frac { 1 } { 3 } ) ^ { 7 } ] ^ { 2 } - \frac { 5 } { 4 } =$$

Evaluate

$$\frac{5}{9}\approx 0.555555556$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 4 and 6 to get 24.

$$\frac{20}{4^{2}}+\frac{\left(\frac{2}{3}\right)^{24}}{\left(\left(\frac{2}{3}\right)^{11}\right)^{2}}+\frac{\left(\frac{1}{3}\right)^{16}}{\left(\left(\frac{1}{3}\right)^{7}\right)^{2}}-\frac{5}{4}$$

To raise a power to another power, multiply the exponents. Multiply 11 and 2 to get 22.

$$\frac{20}{4^{2}}+\frac{\left(\frac{2}{3}\right)^{24}}{\left(\frac{2}{3}\right)^{22}}+\frac{\left(\frac{1}{3}\right)^{16}}{\left(\left(\frac{1}{3}\right)^{7}\right)^{2}}-\frac{5}{4}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 22 from 24 to get 2.

$$\frac{20}{4^{2}}+\left(\frac{2}{3}\right)^{2}+\frac{\left(\frac{1}{3}\right)^{16}}{\left(\left(\frac{1}{3}\right)^{7}\right)^{2}}-\frac{5}{4}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{20}{4^{2}}+\left(\frac{2}{3}\right)^{2}+\frac{\left(\frac{1}{3}\right)^{16}}{\left(\frac{1}{3}\right)^{14}}-\frac{5}{4}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 14 from 16 to get 2.

$$\frac{20}{4^{2}}+\left(\frac{2}{3}\right)^{2}+\left(\frac{1}{3}\right)^{2}-\frac{5}{4}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{20}{16}+\left(\frac{2}{3}\right)^{2}+\left(\frac{1}{3}\right)^{2}-\frac{5}{4}$$

Reduce the fraction \frac{20}{16} to lowest terms by extracting and canceling out 4.

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

Calculate \frac{2}{3} to the power of 2 and get \frac{4}{9}.

$$\frac{5}{4}+\frac{4}{9}+\left(\frac{1}{3}\right)^{2}-\frac{5}{4}$$

Add \frac{5}{4} and \frac{4}{9} to get \frac{61}{36}.

$$\frac{61}{36}+\left(\frac{1}{3}\right)^{2}-\frac{5}{4}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{61}{36}+\frac{1}{9}-\frac{5}{4}$$

Add \frac{61}{36} and \frac{1}{9} to get \frac{65}{36}.

$$\frac{65}{36}-\frac{5}{4}$$

Subtract \frac{5}{4} from \frac{65}{36} to get \frac{5}{9}.

$$\frac{5}{9}$$

Factor

$$\frac{5}{3 ^ {2}} = 0.5555555555555556$$