Solve 22/7*2.25*2.25*10/frac{4{3}*22/7*0.75*0.75*0.75}

$$\frac { \frac { 22 } { 7 } \times 2.25 \times 2.25 \times 10 } { \frac { 4 } { 3 } \times \frac { 22 } { 7 } \times 0.75 \times 0.75 \times 0.75 }$$

Evaluate

$$90$$

Solution Steps

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{2.25\times 2.25\times 10}{0.75\times 0.75\times 0.75\times \frac{4}{3}\times \left(\frac{22}{7}\right)^{0}}$$

Multiply 2.25 and 2.25 to get 5.0625.

$$\frac{5.0625\times 10}{0.75\times 0.75\times 0.75\times \frac{4}{3}\times \left(\frac{22}{7}\right)^{0}}$$

Multiply 5.0625 and 10 to get 50.625.

$$\frac{50.625}{0.75\times 0.75\times 0.75\times \frac{4}{3}\times \left(\frac{22}{7}\right)^{0}}$$

Multiply 0.75 and 0.75 to get 0.5625.

$$\frac{50.625}{0.5625\times 0.75\times \frac{4}{3}\times \left(\frac{22}{7}\right)^{0}}$$

Multiply 0.5625 and 0.75 to get 0.421875.

$$\frac{50.625}{0.421875\times \frac{4}{3}\times \left(\frac{22}{7}\right)^{0}}$$

Convert decimal number 0.421875 to fraction \frac{421875}{1000000}. Reduce the fraction \frac{421875}{1000000} to lowest terms by extracting and canceling out 15625.

$$\frac{50.625}{\frac{27}{64}\times \frac{4}{3}\times \left(\frac{22}{7}\right)^{0}}$$

Multiply \frac{27}{64} times \frac{4}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{50.625}{\frac{27\times 4}{64\times 3}\times \left(\frac{22}{7}\right)^{0}}$$

Do the multiplications in the fraction \frac{27\times 4}{64\times 3}.

$$\frac{50.625}{\frac{108}{192}\times \left(\frac{22}{7}\right)^{0}}$$

Reduce the fraction \frac{108}{192} to lowest terms by extracting and canceling out 12.

$$\frac{50.625}{\frac{9}{16}\times \left(\frac{22}{7}\right)^{0}}$$

Calculate \frac{22}{7} to the power of 0 and get 1.

$$\frac{50.625}{\frac{9}{16}\times 1}$$

Multiply \frac{9}{16} and 1 to get \frac{9}{16}.

$$\frac{50.625}{\frac{9}{16}}$$

Divide 50.625 by \frac{9}{16} by multiplying 50.625 by the reciprocal of \frac{9}{16}.

$$50.625\times \frac{16}{9}$$

Convert decimal number 50.625 to fraction \frac{50625}{1000}. Reduce the fraction \frac{50625}{1000} to lowest terms by extracting and canceling out 125.

$$\frac{405}{8}\times \frac{16}{9}$$

Multiply \frac{405}{8} times \frac{16}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{405\times 16}{8\times 9}$$

Do the multiplications in the fraction \frac{405\times 16}{8\times 9}.

$$\frac{6480}{72}$$

Divide 6480 by 72 to get 90.

$$90$$

Factor

$$2\times 5\times 3^{2}$$