Solve sqrt[3]{frac{sqrt{27^2}}{3^6*5^3}}

$$\sqrt[ 3 ] { \frac { \sqrt { 27 ^ { 2 } } } { 3 ^ { 6 } \times 5 ^ { 3 } } }$$

Evaluate

$$\frac{1}{15}\approx 0.066666667$$

Solution Steps

Calculate 27 to the power of 2 and get 729.

$$\sqrt[3]{\frac{\sqrt{729}}{3^{6}\times 5^{3}}}$$

Calculate the square root of 729 and get 27.

$$\sqrt[3]{\frac{27}{3^{6}\times 5^{3}}}$$

Calculate 3 to the power of 6 and get 729.

$$\sqrt[3]{\frac{27}{729\times 5^{3}}}$$

Calculate 5 to the power of 3 and get 125.

$$\sqrt[3]{\frac{27}{729\times 125}}$$

Multiply 729 and 125 to get 91125.

$$\sqrt[3]{\frac{27}{91125}}$$

Reduce the fraction \frac{27}{91125} to lowest terms by extracting and canceling out 27.

$$\sqrt[3]{\frac{1}{3375}}$$

Calculate \sqrt[3]{\frac{1}{3375}} and get \frac{1}{15}.

$$\frac{1}{15}$$

Factor

$$\frac{1}{3 \cdot 5} = 0.06666666666666667$$