Solve frac{sqrt{25}x}{6}-(5/8)^3

$$\frac { \sqrt { 25 } x } { 6 } - ( \frac { 5 } { 8 } ) ^ { 3 }$$

Evaluate

$$\frac{5x}{6}-\frac{125}{512}$$

Short Solution Steps

Calculate the square root of 25 and get 5.

$$\frac{5x}{6}-\left(\frac{5}{8}\right)^{3}$$

Calculate \frac{5}{8} to the power of 3 and get \frac{125}{512}.

$$\frac{5x}{6}-\frac{125}{512}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 512 is 1536. Multiply \frac{5x}{6} times \frac{256}{256}. Multiply \frac{125}{512} times \frac{3}{3}.

$$\frac{256\times 5x}{1536}-\frac{125\times 3}{1536}$$

Since \frac{256\times 5x}{1536} and \frac{125\times 3}{1536} have the same denominator, subtract them by subtracting their numerators.

$$\frac{256\times 5x-125\times 3}{1536}$$

Do the multiplications in 256\times 5x-125\times 3.

$$\frac{1280x-375}{1536}$$

Factor

$$\frac{5\left(256x-75\right)}{1536}$$

Solution Steps

Calculate the square root of 25 and get 5.

$$factor(\frac{5x}{6}-\left(\frac{5}{8}\right)^{3})$$

Calculate \frac{5}{8} to the power of 3 and get \frac{125}{512}.

$$factor(\frac{5x}{6}-\frac{125}{512})$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 6 and 512 is 1536. Multiply \frac{5x}{6} times \frac{256}{256}. Multiply \frac{125}{512} times \frac{3}{3}.

$$factor(\frac{256\times 5x}{1536}-\frac{125\times 3}{1536})$$

Since \frac{256\times 5x}{1536} and \frac{125\times 3}{1536} have the same denominator, subtract them by subtracting their numerators.

$$factor(\frac{256\times 5x-125\times 3}{1536})$$

Do the multiplications in 256\times 5x-125\times 3.

$$factor(\frac{1280x-375}{1536})$$

Consider 1280x-375. Factor out 5.

$$5\left(256x-75\right)$$

Rewrite the complete factored expression. Simplify.

$$\frac{5\left(256x-75\right)}{1536}$$