Solve [(5/3)^{2}:(10/9)^{2}]^2:1/2+(4/3)^-1+2^-3:2^-2=

$$[ ( \frac { 5 } { 3 } ) ^ { 2 } : ( \frac { 10 } { 9 } ) ^ { 2 } ] ^ { 2 } : \frac { 1 } { 2 } + ( \frac { 4 } { 3 } ) ^ { - 1 } + 2 ^ { - 3 } : 2 ^ { - 2 } =$$

Evaluate

$$\frac{91}{8}=11.375$$

Solution Steps

Rewrite 2^{-2} as 2\times 2^{-3}. Cancel out 2^{-3} in both numerator and denominator.

$$\frac{\left(\frac{\left(\frac{5}{3}\right)^{2}}{\left(\frac{10}{9}\right)^{2}}\right)^{2}}{\frac{1}{2}}+\left(\frac{4}{3}\right)^{-1}+\frac{1}{2}$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$\frac{\left(\frac{\frac{25}{9}}{\left(\frac{10}{9}\right)^{2}}\right)^{2}}{\frac{1}{2}}+\left(\frac{4}{3}\right)^{-1}+\frac{1}{2}$$

Calculate \frac{10}{9} to the power of 2 and get \frac{100}{81}.

$$\frac{\left(\frac{\frac{25}{9}}{\frac{100}{81}}\right)^{2}}{\frac{1}{2}}+\left(\frac{4}{3}\right)^{-1}+\frac{1}{2}$$

Divide \frac{25}{9} by \frac{100}{81} by multiplying \frac{25}{9} by the reciprocal of \frac{100}{81}.

$$\frac{\left(\frac{25}{9}\times \frac{81}{100}\right)^{2}}{\frac{1}{2}}+\left(\frac{4}{3}\right)^{-1}+\frac{1}{2}$$

Multiply \frac{25}{9} and \frac{81}{100} to get \frac{9}{4}.

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

Calculate \frac{9}{4} to the power of 2 and get \frac{81}{16}.

$$\frac{\frac{81}{16}}{\frac{1}{2}}+\left(\frac{4}{3}\right)^{-1}+\frac{1}{2}$$

Divide \frac{81}{16} by \frac{1}{2} by multiplying \frac{81}{16} by the reciprocal of \frac{1}{2}.

$$\frac{81}{16}\times 2+\left(\frac{4}{3}\right)^{-1}+\frac{1}{2}$$

Multiply \frac{81}{16} and 2 to get \frac{81}{8}.

$$\frac{81}{8}+\left(\frac{4}{3}\right)^{-1}+\frac{1}{2}$$

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

$$\frac{81}{8}+\frac{3}{4}+\frac{1}{2}$$

Add \frac{81}{8} and \frac{3}{4} to get \frac{87}{8}.

$$\frac{87}{8}+\frac{1}{2}$$

Add \frac{87}{8} and \frac{1}{2} to get \frac{91}{8}.

$$\frac{91}{8}$$

Factor

$$\frac{7 \cdot 13}{2 ^ {3}} = 11\frac{3}{8} = 11.375$$