Solve {left(-4/3right)}^2*0.3^4-{left(-1/2right)}^3*{left(4/3right)}^2

$${ \left(- \frac{ 4 }{ 3 } \right) }^{ 2 } \times { 0.3 }^{ 4 } - { \left(- \frac{ 1 }{ 2 } \right) }^{ 3 } \times { \left( \frac{ 4 }{ 3 } \right) }^{ 2 }$$

Evaluate

$$\frac{1331}{5625}\approx 0.236622222$$

Solution Steps

Calculate -\frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{16}{9}\times 0.3^{4}-\left(-\frac{1}{2}\right)^{3}\times \left(\frac{4}{3}\right)^{2}$$

Calculate 0.3 to the power of 4 and get 0.0081.

$$\frac{16}{9}\times 0.0081-\left(-\frac{1}{2}\right)^{3}\times \left(\frac{4}{3}\right)^{2}$$

Convert decimal number 0.0081 to fraction \frac{81}{10000}.

$$\frac{16}{9}\times \frac{81}{10000}-\left(-\frac{1}{2}\right)^{3}\times \left(\frac{4}{3}\right)^{2}$$

Multiply \frac{16}{9} times \frac{81}{10000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16\times 81}{9\times 10000}-\left(-\frac{1}{2}\right)^{3}\times \left(\frac{4}{3}\right)^{2}$$

Do the multiplications in the fraction \frac{16\times 81}{9\times 10000}.

$$\frac{1296}{90000}-\left(-\frac{1}{2}\right)^{3}\times \left(\frac{4}{3}\right)^{2}$$

Reduce the fraction \frac{1296}{90000} to lowest terms by extracting and canceling out 144.

$$\frac{9}{625}-\left(-\frac{1}{2}\right)^{3}\times \left(\frac{4}{3}\right)^{2}$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$\frac{9}{625}-\left(-\frac{1}{8}\times \left(\frac{4}{3}\right)^{2}\right)$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{9}{625}-\left(-\frac{1}{8}\times \frac{16}{9}\right)$$

Multiply -\frac{1}{8} times \frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9}{625}-\frac{-16}{8\times 9}$$

Do the multiplications in the fraction \frac{-16}{8\times 9}.

$$\frac{9}{625}-\frac{-16}{72}$$

Reduce the fraction \frac{-16}{72} to lowest terms by extracting and canceling out 8.

$$\frac{9}{625}-\left(-\frac{2}{9}\right)$$

The opposite of -\frac{2}{9} is \frac{2}{9}.

$$\frac{9}{625}+\frac{2}{9}$$

Least common multiple of 625 and 9 is 5625. Convert \frac{9}{625} and \frac{2}{9} to fractions with denominator 5625.

$$\frac{81}{5625}+\frac{1250}{5625}$$

Since \frac{81}{5625} and \frac{1250}{5625} have the same denominator, add them by adding their numerators.

$$\frac{81+1250}{5625}$$

Add 81 and 1250 to get 1331.

$$\frac{1331}{5625}$$

Factor

$$\frac{11 ^ {3}}{3 ^ {2} \cdot 5 ^ {4}} = 0.23662222222222223$$