Solve 10^2/20^415^2/126^2/{45^2}

$$\frac{ { 10 }^{ 2 } }{ { 20 }^{ 4 } } \frac{ { 15 }^{ 2 } }{ 12 } \frac{ { 6 }^{ 2 } }{ { 45 }^{ 2 } }$$

Evaluate

$$\frac{1}{4800}\approx 0.000208333$$

Solution Steps

Calculate 10 to the power of 2 and get 100.

$$\frac{100}{20^{4}}\times \frac{15^{2}}{12}\times \frac{6^{2}}{45^{2}}$$

Calculate 20 to the power of 4 and get 160000.

$$\frac{100}{160000}\times \frac{15^{2}}{12}\times \frac{6^{2}}{45^{2}}$$

Reduce the fraction \frac{100}{160000} to lowest terms by extracting and canceling out 100.

$$\frac{1}{1600}\times \frac{15^{2}}{12}\times \frac{6^{2}}{45^{2}}$$

Calculate 15 to the power of 2 and get 225.

$$\frac{1}{1600}\times \frac{225}{12}\times \frac{6^{2}}{45^{2}}$$

Reduce the fraction \frac{225}{12} to lowest terms by extracting and canceling out 3.

$$\frac{1}{1600}\times \frac{75}{4}\times \frac{6^{2}}{45^{2}}$$

Multiply \frac{1}{1600} times \frac{75}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 75}{1600\times 4}\times \frac{6^{2}}{45^{2}}$$

Do the multiplications in the fraction \frac{1\times 75}{1600\times 4}.

$$\frac{75}{6400}\times \frac{6^{2}}{45^{2}}$$

Reduce the fraction \frac{75}{6400} to lowest terms by extracting and canceling out 25.

$$\frac{3}{256}\times \frac{6^{2}}{45^{2}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{3}{256}\times \frac{36}{45^{2}}$$

Calculate 45 to the power of 2 and get 2025.

$$\frac{3}{256}\times \frac{36}{2025}$$

Reduce the fraction \frac{36}{2025} to lowest terms by extracting and canceling out 9.

$$\frac{3}{256}\times \frac{4}{225}$$

Multiply \frac{3}{256} times \frac{4}{225} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 4}{256\times 225}$$

Do the multiplications in the fraction \frac{3\times 4}{256\times 225}.

$$\frac{12}{57600}$$

Reduce the fraction \frac{12}{57600} to lowest terms by extracting and canceling out 12.

$$\frac{1}{4800}$$

Factor

$$\frac{1}{2 ^ {6} \cdot 3 \cdot 5 ^ {2}} = 0.00020833333333333335$$