Solve -(5/3)^3-2(5/3)^2+15

$$- ( \frac { 5 } { 3 } ) ^ { 3 } - 2 ( \frac { 5 } { 3 } ) ^ { 2 } + 15$$

Evaluate

$$\frac{130}{27}\approx 4.814814815$$

Solution Steps

Calculate \frac{5}{3} to the power of 3 and get \frac{125}{27}.

$$-\frac{125}{27}-2\times \left(\frac{5}{3}\right)^{2}+15$$

Calculate \frac{5}{3} to the power of 2 and get \frac{25}{9}.

$$-\frac{125}{27}-2\times \frac{25}{9}+15$$

Express 2\times \frac{25}{9} as a single fraction.

$$-\frac{125}{27}-\frac{2\times 25}{9}+15$$

Multiply 2 and 25 to get 50.

$$-\frac{125}{27}-\frac{50}{9}+15$$

Least common multiple of 27 and 9 is 27. Convert -\frac{125}{27} and \frac{50}{9} to fractions with denominator 27.

$$-\frac{125}{27}-\frac{150}{27}+15$$

Since -\frac{125}{27} and \frac{150}{27} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-125-150}{27}+15$$

Subtract 150 from -125 to get -275.

$$-\frac{275}{27}+15$$

Convert 15 to fraction \frac{405}{27}.

$$-\frac{275}{27}+\frac{405}{27}$$

Since -\frac{275}{27} and \frac{405}{27} have the same denominator, add them by adding their numerators.

$$\frac{-275+405}{27}$$

Add -275 and 405 to get 130.

$$\frac{130}{27}$$

Factor

$$\frac{2 \cdot 5 \cdot 13}{3 ^ {3}} = 4\frac{22}{27} = 4.814814814814815$$