Solve 3^5/7^5*7^4/3^8

$$\frac { 3 ^ { 5 } } { 7 ^ { 5 } } \times \frac { 7 ^ { 4 } } { 3 ^ { 8 } }$$

Evaluate

$$\frac{1}{189}\approx 0.005291005$$

Solution Steps

Calculate 3 to the power of 5 and get 243.

$$\frac{243}{7^{5}}\times \frac{7^{4}}{3^{8}}$$

Calculate 7 to the power of 5 and get 16807.

$$\frac{243}{16807}\times \frac{7^{4}}{3^{8}}$$

Calculate 7 to the power of 4 and get 2401.

$$\frac{243}{16807}\times \frac{2401}{3^{8}}$$

Calculate 3 to the power of 8 and get 6561.

$$\frac{243}{16807}\times \frac{2401}{6561}$$

Multiply \frac{243}{16807} times \frac{2401}{6561} by multiplying numerator times numerator and denominator times denominator.

$$\frac{243\times 2401}{16807\times 6561}$$

Do the multiplications in the fraction \frac{243\times 2401}{16807\times 6561}.

$$\frac{583443}{110270727}$$

Reduce the fraction \frac{583443}{110270727} to lowest terms by extracting and canceling out 583443.

$$\frac{1}{189}$$

Factor

$$\frac{1}{3 ^ {3} \cdot 7} = 0.005291005291005291$$