Solve (2/3)(2/2)/(frac{3{2})^-5(2/3)^3(frac{2}{3})^10(frac{2}{3})^9}

$$\frac { ( \frac { 2 } { 3 } ) ( \frac { 2 } { 2 } ) } { ( \frac { 3 } { 2 } ) ^ { - 5 } ( \frac { 2 } { 3 } ) ^ { 3 } ( \frac { 2 } { 3 } ) ^ { 10 } ( \frac { 2 } { 3 } ) ^ { 9 } }$$

Evaluate

$$\frac{2541865828329}{67108864}=37876.752441064$$

Solution Steps

Divide 2 by 2 to get 1.

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

To multiply powers of the same base, add their exponents. Add 3 and 10 to get 13.

$$\frac{\frac{2}{3}\times 1}{\left(\frac{3}{2}\right)^{-5}\times \left(\frac{2}{3}\right)^{13}\times \left(\frac{2}{3}\right)^{9}}$$

To multiply powers of the same base, add their exponents. Add 13 and 9 to get 22.

$$\frac{\frac{2}{3}\times 1}{\left(\frac{3}{2}\right)^{-5}\times \left(\frac{2}{3}\right)^{22}}$$

Cancel out \frac{2}{3} in both numerator and denominator.

$$\frac{1}{\left(\frac{2}{3}\right)^{21}\times \left(\frac{3}{2}\right)^{-5}}$$

Calculate \frac{2}{3} to the power of 21 and get \frac{2097152}{10460353203}.

$$\frac{1}{\frac{2097152}{10460353203}\times \left(\frac{3}{2}\right)^{-5}}$$

Calculate \frac{3}{2} to the power of -5 and get \frac{32}{243}.

$$\frac{1}{\frac{2097152}{10460353203}\times \frac{32}{243}}$$

Multiply \frac{2097152}{10460353203} and \frac{32}{243} to get \frac{67108864}{2541865828329}.

$$\frac{1}{\frac{67108864}{2541865828329}}$$

Divide 1 by \frac{67108864}{2541865828329} by multiplying 1 by the reciprocal of \frac{67108864}{2541865828329}.

$$1\times \frac{2541865828329}{67108864}$$

Multiply 1 and \frac{2541865828329}{67108864} to get \frac{2541865828329}{67108864}.

$$\frac{2541865828329}{67108864}$$

Factor

$$\frac{3 ^ {26}}{2 ^ {26}} = 37876\frac{50495465}{67108864} = 37876.75244106352$$