Solve (frac{-3^{4}*(3sqrt{5})^{0}*(3^{-1}*5^{-2})^2}{(-3)^5*5^-7})^-frac{2{3}}=

$$( \frac { - 3 ^ { 4 } \cdot ( 3 \sqrt { 5 } ) ^ { 0 } \cdot ( 3 ^ { - 1 } \cdot 5 ^ { - 2 } ) ^ { 2 } } { ( - 3 ) ^ { 5 } \cdot 5 ^ { - 7 } } ) ^ { - \frac { 2 } { 3 } } =$$

Evaluate

$$\frac{9}{25}=0.36$$

Solution Steps

Calculate 3 to the power of 4 and get 81.

$$\left(\frac{-81\times \left(3\sqrt{5}\right)^{0}\times \left(3^{-1}\times 5^{-2}\right)^{2}}{\left(-3\right)^{5}\times 5^{-7}}\right)^{-\frac{2}{3}}$$

Calculate 3\sqrt{5} to the power of 0 and get 1.

$$\left(\frac{-81\times \left(3^{-1}\times 5^{-2}\right)^{2}}{\left(-3\right)^{5}\times 5^{-7}}\right)^{-\frac{2}{3}}$$

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

$$\left(\frac{-81\times \left(\frac{1}{3}\times 5^{-2}\right)^{2}}{\left(-3\right)^{5}\times 5^{-7}}\right)^{-\frac{2}{3}}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\left(\frac{-81\times \left(\frac{1}{3}\times \frac{1}{25}\right)^{2}}{\left(-3\right)^{5}\times 5^{-7}}\right)^{-\frac{2}{3}}$$

Multiply \frac{1}{3} and \frac{1}{25} to get \frac{1}{75}.

$$\left(\frac{-81\times \left(\frac{1}{75}\right)^{2}}{\left(-3\right)^{5}\times 5^{-7}}\right)^{-\frac{2}{3}}$$

Calculate \frac{1}{75} to the power of 2 and get \frac{1}{5625}.

$$\left(\frac{-81\times \frac{1}{5625}}{\left(-3\right)^{5}\times 5^{-7}}\right)^{-\frac{2}{3}}$$

Multiply -81 and \frac{1}{5625} to get -\frac{9}{625}.

$$\left(\frac{-\frac{9}{625}}{\left(-3\right)^{5}\times 5^{-7}}\right)^{-\frac{2}{3}}$$

Calculate -3 to the power of 5 and get -243.

$$\left(\frac{-\frac{9}{625}}{-243\times 5^{-7}}\right)^{-\frac{2}{3}}$$

Calculate 5 to the power of -7 and get \frac{1}{78125}.

$$\left(\frac{-\frac{9}{625}}{-243\times \frac{1}{78125}}\right)^{-\frac{2}{3}}$$

Multiply -243 and \frac{1}{78125} to get -\frac{243}{78125}.

$$\left(\frac{-\frac{9}{625}}{-\frac{243}{78125}}\right)^{-\frac{2}{3}}$$

Divide -\frac{9}{625} by -\frac{243}{78125} by multiplying -\frac{9}{625} by the reciprocal of -\frac{243}{78125}.

$$\left(-\frac{9}{625}\left(-\frac{78125}{243}\right)\right)^{-\frac{2}{3}}$$

Multiply -\frac{9}{625} and -\frac{78125}{243} to get \frac{125}{27}.

$$\left(\frac{125}{27}\right)^{-\frac{2}{3}}$$

Calculate \frac{125}{27} to the power of -\frac{2}{3} and get \frac{9}{25}.

$$\frac{9}{25}$$

Factor

$$\frac{3 ^ {2}}{5 ^ {2}} = 0.36$$