Solve frac{(81^{2})^{1/4}*sqrt[5]{32^{3}}*125^frac{2{3}}}{sqrt[3]{27^2}*(2/3)^-3*(9/4)^-2}

$$\frac { ( 81 ^ { 2 } ) ^ { \frac { 1 } { 4 } } \cdot \sqrt[ 5 ] { 32 ^ { 3 } } \cdot 125 ^ { \frac { 2 } { 3 } } } { \sqrt[ 3 ] { 27 ^ { 2 } } \cdot ( \frac { 2 } { 3 } ) ^ { - 3 } \cdot ( \frac { 9 } { 4 } ) ^ { - 2 } }$$

Evaluate

$$300$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{1}{4} to get \frac{1}{2}.

$$\frac{81^{\frac{1}{2}}\sqrt[5]{32^{3}}\times 125^{\frac{2}{3}}}{\sqrt[3]{27^{2}}\times \left(\frac{2}{3}\right)^{-3}\times \left(\frac{9}{4}\right)^{-2}}$$

Calculate 81 to the power of \frac{1}{2} and get 9.

$$\frac{9\sqrt[5]{32^{3}}\times 125^{\frac{2}{3}}}{\sqrt[3]{27^{2}}\times \left(\frac{2}{3}\right)^{-3}\times \left(\frac{9}{4}\right)^{-2}}$$

Calculate 32 to the power of 3 and get 32768.

$$\frac{9\sqrt[5]{32768}\times 125^{\frac{2}{3}}}{\sqrt[3]{27^{2}}\times \left(\frac{2}{3}\right)^{-3}\times \left(\frac{9}{4}\right)^{-2}}$$

Calculate \sqrt[5]{32768} and get 8.

$$\frac{9\times 8\times 125^{\frac{2}{3}}}{\sqrt[3]{27^{2}}\times \left(\frac{2}{3}\right)^{-3}\times \left(\frac{9}{4}\right)^{-2}}$$

Multiply 9 and 8 to get 72.

$$\frac{72\times 125^{\frac{2}{3}}}{\sqrt[3]{27^{2}}\times \left(\frac{2}{3}\right)^{-3}\times \left(\frac{9}{4}\right)^{-2}}$$

Calculate 125 to the power of \frac{2}{3} and get 25.

$$\frac{72\times 25}{\sqrt[3]{27^{2}}\times \left(\frac{2}{3}\right)^{-3}\times \left(\frac{9}{4}\right)^{-2}}$$

Multiply 72 and 25 to get 1800.

$$\frac{1800}{\sqrt[3]{27^{2}}\times \left(\frac{2}{3}\right)^{-3}\times \left(\frac{9}{4}\right)^{-2}}$$

Calculate 27 to the power of 2 and get 729.

$$\frac{1800}{\sqrt[3]{729}\times \left(\frac{2}{3}\right)^{-3}\times \left(\frac{9}{4}\right)^{-2}}$$

Calculate \sqrt[3]{729} and get 9.

$$\frac{1800}{9\times \left(\frac{2}{3}\right)^{-3}\times \left(\frac{9}{4}\right)^{-2}}$$

Calculate \frac{2}{3} to the power of -3 and get \frac{27}{8}.

$$\frac{1800}{9\times \frac{27}{8}\times \left(\frac{9}{4}\right)^{-2}}$$

Multiply 9 and \frac{27}{8} to get \frac{243}{8}.

$$\frac{1800}{\frac{243}{8}\times \left(\frac{9}{4}\right)^{-2}}$$

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

$$\frac{1800}{\frac{243}{8}\times \frac{16}{81}}$$

Multiply \frac{243}{8} and \frac{16}{81} to get 6.

$$\frac{1800}{6}$$

Divide 1800 by 6 to get 300.

$$300$$

Factor

$$2^{2}\times 3\times 5^{2}$$