Solve 45*30/100*22/7[(1.4)^2*2.2+4/3*(1.4)^3]

$$45 \times \frac { 30 } { 100 } \times \frac { 22 } { 7 } [ ( 1.4 ) ^ { 2 } \times 2.2 + \frac { 4 } { 3 } \times ( 1.4 ) ^ { 3 } ]$$

Evaluate

$$338.184$$

Solution Steps

Reduce the fraction \frac{30}{100} to lowest terms by extracting and canceling out 10.

$$45\times \frac{3}{10}\times \frac{22}{7}\left(1.4^{2}\times 2.2+\frac{4}{3}\times 1.4^{3}\right)$$

Express 45\times \frac{3}{10} as a single fraction.

$$\frac{45\times 3}{10}\times \frac{22}{7}\left(1.4^{2}\times 2.2+\frac{4}{3}\times 1.4^{3}\right)$$

Multiply 45 and 3 to get 135.

$$\frac{135}{10}\times \frac{22}{7}\left(1.4^{2}\times 2.2+\frac{4}{3}\times 1.4^{3}\right)$$

Reduce the fraction \frac{135}{10} to lowest terms by extracting and canceling out 5.

$$\frac{27}{2}\times \frac{22}{7}\left(1.4^{2}\times 2.2+\frac{4}{3}\times 1.4^{3}\right)$$

Multiply \frac{27}{2} times \frac{22}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{27\times 22}{2\times 7}\left(1.4^{2}\times 2.2+\frac{4}{3}\times 1.4^{3}\right)$$

Do the multiplications in the fraction \frac{27\times 22}{2\times 7}.

$$\frac{594}{14}\left(1.4^{2}\times 2.2+\frac{4}{3}\times 1.4^{3}\right)$$

Reduce the fraction \frac{594}{14} to lowest terms by extracting and canceling out 2.

$$\frac{297}{7}\left(1.4^{2}\times 2.2+\frac{4}{3}\times 1.4^{3}\right)$$

Calculate 1.4 to the power of 2 and get 1.96.

$$\frac{297}{7}\left(1.96\times 2.2+\frac{4}{3}\times 1.4^{3}\right)$$

Multiply 1.96 and 2.2 to get 4.312.

$$\frac{297}{7}\left(4.312+\frac{4}{3}\times 1.4^{3}\right)$$

Calculate 1.4 to the power of 3 and get 2.744.

$$\frac{297}{7}\left(4.312+\frac{4}{3}\times 2.744\right)$$

Convert decimal number 2.744 to fraction \frac{2744}{1000}. Reduce the fraction \frac{2744}{1000} to lowest terms by extracting and canceling out 8.

$$\frac{297}{7}\left(4.312+\frac{4}{3}\times \frac{343}{125}\right)$$

Multiply \frac{4}{3} times \frac{343}{125} by multiplying numerator times numerator and denominator times denominator.

$$\frac{297}{7}\left(4.312+\frac{4\times 343}{3\times 125}\right)$$

Do the multiplications in the fraction \frac{4\times 343}{3\times 125}.

$$\frac{297}{7}\left(4.312+\frac{1372}{375}\right)$$

Convert decimal number 4.312 to fraction \frac{4312}{1000}. Reduce the fraction \frac{4312}{1000} to lowest terms by extracting and canceling out 8.

$$\frac{297}{7}\left(\frac{539}{125}+\frac{1372}{375}\right)$$

Least common multiple of 125 and 375 is 375. Convert \frac{539}{125} and \frac{1372}{375} to fractions with denominator 375.

$$\frac{297}{7}\left(\frac{1617}{375}+\frac{1372}{375}\right)$$

Since \frac{1617}{375} and \frac{1372}{375} have the same denominator, add them by adding their numerators.

$$\frac{297}{7}\times \frac{1617+1372}{375}$$

Add 1617 and 1372 to get 2989.

$$\frac{297}{7}\times \frac{2989}{375}$$

Multiply \frac{297}{7} times \frac{2989}{375} by multiplying numerator times numerator and denominator times denominator.

$$\frac{297\times 2989}{7\times 375}$$

Do the multiplications in the fraction \frac{297\times 2989}{7\times 375}.

$$\frac{887733}{2625}$$

Reduce the fraction \frac{887733}{2625} to lowest terms by extracting and canceling out 21.

$$\frac{42273}{125}$$

Factor

$$\frac{7 \cdot 11 \cdot 61 \cdot 3 ^ {2}}{5 ^ {3}} = 338\frac{23}{125} = 338.184$$