Solve pi/5-(2/x^2)^3

$$\frac { \pi } { 5 } - ( \frac { 2 } { x ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$\frac{\pi }{5}-\frac{8}{x^{6}}$$

Short Solution Steps

To raise \frac{2}{x^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\pi }{5}-\frac{2^{3}}{\left(x^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\pi }{5}-\frac{2^{3}}{x^{6}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\pi }{5}-\frac{8}{x^{6}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and x^{6} is 5x^{6}. Multiply \frac{\pi }{5} times \frac{x^{6}}{x^{6}}. Multiply \frac{8}{x^{6}} times \frac{5}{5}.

$$\frac{\pi x^{6}}{5x^{6}}-\frac{8\times 5}{5x^{6}}$$

Since \frac{\pi x^{6}}{5x^{6}} and \frac{8\times 5}{5x^{6}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\pi x^{6}-8\times 5}{5x^{6}}$$

Do the multiplications in \pi x^{6}-8\times 5.

$$\frac{\pi x^{6}-40}{5x^{6}}$$

Expand

$$\frac{\pi }{5}-\frac{8}{x^{6}}$$

Short Solution Steps

To raise \frac{2}{x^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\pi }{5}-\frac{2^{3}}{\left(x^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\pi }{5}-\frac{2^{3}}{x^{6}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\pi }{5}-\frac{8}{x^{6}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and x^{6} is 5x^{6}. Multiply \frac{\pi }{5} times \frac{x^{6}}{x^{6}}. Multiply \frac{8}{x^{6}} times \frac{5}{5}.

$$\frac{\pi x^{6}}{5x^{6}}-\frac{8\times 5}{5x^{6}}$$

Since \frac{\pi x^{6}}{5x^{6}} and \frac{8\times 5}{5x^{6}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\pi x^{6}-8\times 5}{5x^{6}}$$

Do the multiplications in \pi x^{6}-8\times 5.

$$\frac{\pi x^{6}-40}{5x^{6}}$$