Solve [(1/3)^{2}*(1/3)^{2}]^{2}:(1/3)^{7}+[(1/6)^{5}*(frac{1}{6})^3*(frac{1}{6})^2]^2:(frac{1}{6})^19=

$$[ ( \frac { 1 } { 3 } ) ^ { 2 } \cdot ( \frac { 1 } { 3 } ) ^ { 2 } ] ^ { 2 } : ( \frac { 1 } { 3 } ) ^ { 7 } + [ ( \frac { 1 } { 6 } ) ^ { 5 } \cdot ( \frac { 1 } { 6 } ) ^ { 3 } \cdot ( \frac { 1 } { 6 } ) ^ { 2 } ] ^ { 2 } : ( \frac { 1 } { 6 } ) ^ { 19 } =$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\left(\left(\frac{1}{3}\right)^{4}\right)^{2}}{\left(\frac{1}{3}\right)^{7}}+\frac{\left(\left(\frac{1}{6}\right)^{5}\times \left(\frac{1}{6}\right)^{3}\times \left(\frac{1}{6}\right)^{2}\right)^{2}}{\left(\frac{1}{6}\right)^{19}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(\frac{1}{3}\right)^{8}}{\left(\frac{1}{3}\right)^{7}}+\frac{\left(\left(\frac{1}{6}\right)^{5}\times \left(\frac{1}{6}\right)^{3}\times \left(\frac{1}{6}\right)^{2}\right)^{2}}{\left(\frac{1}{6}\right)^{19}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 8 to get 1.

$$\left(\frac{1}{3}\right)^{1}+\frac{\left(\left(\frac{1}{6}\right)^{5}\times \left(\frac{1}{6}\right)^{3}\times \left(\frac{1}{6}\right)^{2}\right)^{2}}{\left(\frac{1}{6}\right)^{19}}$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$\left(\frac{1}{3}\right)^{1}+\frac{\left(\left(\frac{1}{6}\right)^{8}\times \left(\frac{1}{6}\right)^{2}\right)^{2}}{\left(\frac{1}{6}\right)^{19}}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$\left(\frac{1}{3}\right)^{1}+\frac{\left(\left(\frac{1}{6}\right)^{10}\right)^{2}}{\left(\frac{1}{6}\right)^{19}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 2 to get 20.

$$\left(\frac{1}{3}\right)^{1}+\frac{\left(\frac{1}{6}\right)^{20}}{\left(\frac{1}{6}\right)^{19}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 19 from 20 to get 1.

$$\left(\frac{1}{3}\right)^{1}+\left(\frac{1}{6}\right)^{1}$$

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

$$\frac{1}{3}+\left(\frac{1}{6}\right)^{1}$$

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

$$\frac{1}{3}+\frac{1}{6}$$

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

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$