Solve sqrt{(216)^2/3*(25)^1/2/(frac{4{100})^-3/2}}

$$\sqrt { \frac { ( 216 ) ^ { 2 / 3 } \times ( 25 ) ^ { 1 / 2 } } { ( \frac { 4 } { 100 } ) ^ { - 3 / 2 } } }$$

Evaluate

$$\frac{6}{5}=1.2$$

Solution Steps

Calculate 216 to the power of \frac{2}{3} and get 36.

$$\sqrt{\frac{36\times 25^{\frac{1}{2}}}{\left(\frac{4}{100}\right)^{-\frac{3}{2}}}}$$

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

$$\sqrt{\frac{36\times 5}{\left(\frac{4}{100}\right)^{-\frac{3}{2}}}}$$

Multiply 36 and 5 to get 180.

$$\sqrt{\frac{180}{\left(\frac{4}{100}\right)^{-\frac{3}{2}}}}$$

Reduce the fraction \frac{4}{100} to lowest terms by extracting and canceling out 4.

$$\sqrt{\frac{180}{\left(\frac{1}{25}\right)^{-\frac{3}{2}}}}$$

Calculate \frac{1}{25} to the power of -\frac{3}{2} and get 125.

$$\sqrt{\frac{180}{125}}$$

Reduce the fraction \frac{180}{125} to lowest terms by extracting and canceling out 5.

$$\sqrt{\frac{36}{25}}$$

Rewrite the square root of the division \frac{36}{25} as the division of square roots \frac{\sqrt{36}}{\sqrt{25}}. Take the square root of both numerator and denominator.

$$\frac{6}{5}$$

Factor

$$\frac{2 \cdot 3}{5} = 1\frac{1}{5} = 1.2$$