Solve {[(3/4)^3*(3/4)^2]^2:(3/4)^8+3/4}:frac{7}{4}+frac{2}{3}

$$\{ [ ( \frac { 3 } { 4 } ) ^ { 3 } \times ( \frac { 3 } { 4 } ) ^ { 2 } ] ^ { 2 } : ( \frac { 3 } { 4 } ) ^ { 8 } + \frac { 3 } { 4 } \} : \frac { 7 } { 4 } + \frac { 2 } { 3 }$$

Evaluate

$$\frac{17}{12}\approx 1.416666667$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{\frac{\left(\left(\frac{3}{4}\right)^{5}\right)^{2}}{\left(\frac{3}{4}\right)^{8}}+\frac{3}{4}}{\frac{7}{4}}+\frac{2}{3}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{\frac{\left(\frac{3}{4}\right)^{10}}{\left(\frac{3}{4}\right)^{8}}+\frac{3}{4}}{\frac{7}{4}}+\frac{2}{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 8 from 10 to get 2.

$$\frac{\left(\frac{3}{4}\right)^{2}+\frac{3}{4}}{\frac{7}{4}}+\frac{2}{3}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{\frac{9}{16}+\frac{3}{4}}{\frac{7}{4}}+\frac{2}{3}$$

Add \frac{9}{16} and \frac{3}{4} to get \frac{21}{16}.

$$\frac{\frac{21}{16}}{\frac{7}{4}}+\frac{2}{3}$$

Divide \frac{21}{16} by \frac{7}{4} by multiplying \frac{21}{16} by the reciprocal of \frac{7}{4}.

$$\frac{21}{16}\times \frac{4}{7}+\frac{2}{3}$$

Multiply \frac{21}{16} and \frac{4}{7} to get \frac{3}{4}.

$$\frac{3}{4}+\frac{2}{3}$$

Add \frac{3}{4} and \frac{2}{3} to get \frac{17}{12}.

$$\frac{17}{12}$$

Factor

$$\frac{17}{2 ^ {2} \cdot 3} = 1\frac{5}{12} = 1.4166666666666667$$