Solve [(2/3)^{4}*(2/3)^3div(2/3)^5]*(1+1/8)+(frac{3}{4}*frac{5}{6}+frac{3}{16}*frac{2}{3})^2-(5-frac{9}{2})^3=

$$[ ( \frac { 2 } { 3 } ) ^ { 4 } \cdot ( \frac { 2 } { 3 } ) ^ { 3 } \div ( \frac { 2 } { 3 } ) ^ { 5 } ] \cdot ( 1 + \frac { 1 } { 8 } ) + ( \frac { 3 } { 4 } \cdot \frac { 5 } { 6 } + \frac { 3 } { 16 } \cdot \frac { 2 } { 3 } ) ^ { 2 } - ( 5 - \frac { 9 } { 2 } ) ^ { 3 } =$$

Evaluate

$$\frac{15}{16}=0.9375$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\left(\frac{2}{3}\right)^{7}}{\left(\frac{2}{3}\right)^{5}}\left(1+\frac{1}{8}\right)+\left(\frac{3}{4}\times \frac{5}{6}+\frac{3}{16}\times \frac{2}{3}\right)^{2}-\left(5-\frac{9}{2}\right)^{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 7 to get 2.

$$\left(\frac{2}{3}\right)^{2}\left(1+\frac{1}{8}\right)+\left(\frac{3}{4}\times \frac{5}{6}+\frac{3}{16}\times \frac{2}{3}\right)^{2}-\left(5-\frac{9}{2}\right)^{3}$$

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

$$\frac{4}{9}\left(1+\frac{1}{8}\right)+\left(\frac{3}{4}\times \frac{5}{6}+\frac{3}{16}\times \frac{2}{3}\right)^{2}-\left(5-\frac{9}{2}\right)^{3}$$

Add 1 and \frac{1}{8} to get \frac{9}{8}.

$$\frac{4}{9}\times \frac{9}{8}+\left(\frac{3}{4}\times \frac{5}{6}+\frac{3}{16}\times \frac{2}{3}\right)^{2}-\left(5-\frac{9}{2}\right)^{3}$$

Multiply \frac{4}{9} and \frac{9}{8} to get \frac{1}{2}.

$$\frac{1}{2}+\left(\frac{3}{4}\times \frac{5}{6}+\frac{3}{16}\times \frac{2}{3}\right)^{2}-\left(5-\frac{9}{2}\right)^{3}$$

Multiply \frac{3}{4} and \frac{5}{6} to get \frac{5}{8}.

$$\frac{1}{2}+\left(\frac{5}{8}+\frac{3}{16}\times \frac{2}{3}\right)^{2}-\left(5-\frac{9}{2}\right)^{3}$$

Multiply \frac{3}{16} and \frac{2}{3} to get \frac{1}{8}.

$$\frac{1}{2}+\left(\frac{5}{8}+\frac{1}{8}\right)^{2}-\left(5-\frac{9}{2}\right)^{3}$$

Add \frac{5}{8} and \frac{1}{8} to get \frac{3}{4}.

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

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

$$\frac{1}{2}+\frac{9}{16}-\left(5-\frac{9}{2}\right)^{3}$$

Add \frac{1}{2} and \frac{9}{16} to get \frac{17}{16}.

$$\frac{17}{16}-\left(5-\frac{9}{2}\right)^{3}$$

Subtract \frac{9}{2} from 5 to get \frac{1}{2}.

$$\frac{17}{16}-\left(\frac{1}{2}\right)^{3}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{17}{16}-\frac{1}{8}$$

Subtract \frac{1}{8} from \frac{17}{16} to get \frac{15}{16}.

$$\frac{15}{16}$$

Factor

$$\frac{3 \cdot 5}{2 ^ {4}} = 0.9375$$