Solve [3^3/16*(4/3)^3]div(6/5)^2

$$[ \frac { 3 ^ { 3 } } { 16 } \times ( \frac { 4 } { 3 } ) ^ { 3 } ] \div ( \frac { 6 } { 5 } ) ^ { 2 }$$

Evaluate

$$\frac{25}{9}\approx 2.777777778$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\frac{\frac{27}{16}\times \left(\frac{4}{3}\right)^{3}}{\left(\frac{6}{5}\right)^{2}}$$

Calculate \frac{4}{3} to the power of 3 and get \frac{64}{27}.

$$\frac{\frac{27}{16}\times \frac{64}{27}}{\left(\frac{6}{5}\right)^{2}}$$

Multiply \frac{27}{16} times \frac{64}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{27\times 64}{16\times 27}}{\left(\frac{6}{5}\right)^{2}}$$

Cancel out 27 in both numerator and denominator.

$$\frac{\frac{64}{16}}{\left(\frac{6}{5}\right)^{2}}$$

Divide 64 by 16 to get 4.

$$\frac{4}{\left(\frac{6}{5}\right)^{2}}$$

Calculate \frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$\frac{4}{\frac{36}{25}}$$

Divide 4 by \frac{36}{25} by multiplying 4 by the reciprocal of \frac{36}{25}.

$$4\times \frac{25}{36}$$

Express 4\times \frac{25}{36} as a single fraction.

$$\frac{4\times 25}{36}$$

Multiply 4 and 25 to get 100.

$$\frac{100}{36}$$

Reduce the fraction \frac{100}{36} to lowest terms by extracting and canceling out 4.

$$\frac{25}{9}$$

Factor

$$\frac{5 ^ {2}}{3 ^ {2}} = 2\frac{7}{9} = 2.7777777777777777$$