Solve {left(2/3right)}^3{left(3/2right)}^2-sqrt{16}

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

Evaluate

$$-\frac{10}{3}\approx -3.333333333$$

Solution Steps

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$\frac{8}{27}\times \left(\frac{3}{2}\right)^{2}-\sqrt{16}$$

Calculate \frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{8}{27}\times \frac{9}{4}-\sqrt{16}$$

Multiply \frac{8}{27} times \frac{9}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{8\times 9}{27\times 4}-\sqrt{16}$$

Do the multiplications in the fraction \frac{8\times 9}{27\times 4}.

$$\frac{72}{108}-\sqrt{16}$$

Reduce the fraction \frac{72}{108} to lowest terms by extracting and canceling out 36.

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

Calculate the square root of 16 and get 4.

$$\frac{2}{3}-4$$

Convert 4 to fraction \frac{12}{3}.

$$\frac{2}{3}-\frac{12}{3}$$

Since \frac{2}{3} and \frac{12}{3} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2-12}{3}$$

Subtract 12 from 2 to get -10.

$$-\frac{10}{3}$$

Factor

$$-\frac{10}{3} = -3\frac{1}{3} = -3.3333333333333335$$