Solve (2/7^+4/7)-2/3^?

$$( 2 / 7 ^ { + 4 } / 7 ) - 2 / 3 ^ { ? }$$

Evaluate

$$-\frac{33566}{50421}\approx -0.665714682$$

Solution Steps

Calculate \frac{2}{7} to the power of 4 and get \frac{16}{2401}.

$$\frac{\frac{16}{2401}}{7}-\left(\frac{2}{3}\right)^{1}$$

Express \frac{\frac{16}{2401}}{7} as a single fraction.

$$\frac{16}{2401\times 7}-\left(\frac{2}{3}\right)^{1}$$

Multiply 2401 and 7 to get 16807.

$$\frac{16}{16807}-\left(\frac{2}{3}\right)^{1}$$

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

$$\frac{16}{16807}-\frac{2}{3}$$

Least common multiple of 16807 and 3 is 50421. Convert \frac{16}{16807} and \frac{2}{3} to fractions with denominator 50421.

$$\frac{48}{50421}-\frac{33614}{50421}$$

Since \frac{48}{50421} and \frac{33614}{50421} have the same denominator, subtract them by subtracting their numerators.

$$\frac{48-33614}{50421}$$

Subtract 33614 from 48 to get -33566.

$$-\frac{33566}{50421}$$

Factor

$$-\frac{33566}{50421} = -0.6657146823744075$$