Solve (sqrt[4]{81})^-3*sqrt{25}*(sqrt[5]{243})^2

$$( \sqrt[ 4 ] { 81 } ) ^ { - 3 } \times \sqrt { 25 } \times ( \sqrt[ 5 ] { 243 } ) ^ { 2 }$$

Evaluate

$$\frac{5}{3}\approx 1.666666667$$

Solution Steps

Calculate \sqrt[4]{81} and get 3.

$$3^{-3}\sqrt{25}\left(\sqrt[5]{243}\right)^{2}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{1}{27}\sqrt{25}\left(\sqrt[5]{243}\right)^{2}$$

Calculate the square root of 25 and get 5.

$$\frac{1}{27}\times 5\left(\sqrt[5]{243}\right)^{2}$$

Multiply \frac{1}{27} and 5 to get \frac{5}{27}.

$$\frac{5}{27}\left(\sqrt[5]{243}\right)^{2}$$

Calculate \sqrt[5]{243} and get 3.

$$\frac{5}{27}\times 3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{5}{27}\times 9$$

Multiply \frac{5}{27} and 9 to get \frac{5}{3}.

$$\frac{5}{3}$$

Factor

$$\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667$$