Solve 5sqrt{243^-3}

$$5 \sqrt{ { 243 }^{ -3 } }$$

Evaluate

$$\frac{5\sqrt{3}}{6561}\approx 0.001319959$$

Solution Steps

Calculate 243 to the power of -3 and get \frac{1}{14348907}.

$$5\sqrt{\frac{1}{14348907}}$$

Rewrite the square root of the division \sqrt{\frac{1}{14348907}} as the division of square roots \frac{\sqrt{1}}{\sqrt{14348907}}.

$$5\times \frac{\sqrt{1}}{\sqrt{14348907}}$$

Calculate the square root of 1 and get 1.

$$5\times \frac{1}{\sqrt{14348907}}$$

Factor 14348907=2187^{2}\times 3. Rewrite the square root of the product \sqrt{2187^{2}\times 3} as the product of square roots \sqrt{2187^{2}}\sqrt{3}. Take the square root of 2187^{2}.

$$5\times \frac{1}{2187\sqrt{3}}$$

Rationalize the denominator of \frac{1}{2187\sqrt{3}} by multiplying numerator and denominator by \sqrt{3}.

$$5\times \frac{\sqrt{3}}{2187\left(\sqrt{3}\right)^{2}}$$

The square of \sqrt{3} is 3.

$$5\times \frac{\sqrt{3}}{2187\times 3}$$

Multiply 2187 and 3 to get 6561.

$$5\times \frac{\sqrt{3}}{6561}$$

Express 5\times \frac{\sqrt{3}}{6561} as a single fraction.

$$\frac{5\sqrt{3}}{6561}$$