Solve frac{5^{7}}{7^{6}}*(7/5)^6-3^6/2^5*(2/3)^5

$$\frac { 5 ^ { 7 } } { 7 ^ { 6 } } \cdot ( \frac { 7 } { 5 } ) ^ { 6 } - \frac { 3 ^ { 6 } } { 2 ^ { 5 } } \cdot ( \frac { 2 } { 3 } ) ^ { 5 }$$

Evaluate

$$2$$

Solution Steps

Calculate 5 to the power of 7 and get 78125.

$$\frac{78125}{7^{6}}\times \left(\frac{7}{5}\right)^{6}-\frac{3^{6}}{2^{5}}\times \left(\frac{2}{3}\right)^{5}$$

Calculate 7 to the power of 6 and get 117649.

$$\frac{78125}{117649}\times \left(\frac{7}{5}\right)^{6}-\frac{3^{6}}{2^{5}}\times \left(\frac{2}{3}\right)^{5}$$

Calculate \frac{7}{5} to the power of 6 and get \frac{117649}{15625}.

$$\frac{78125}{117649}\times \frac{117649}{15625}-\frac{3^{6}}{2^{5}}\times \left(\frac{2}{3}\right)^{5}$$

Multiply \frac{78125}{117649} times \frac{117649}{15625} by multiplying numerator times numerator and denominator times denominator.

$$\frac{78125\times 117649}{117649\times 15625}-\frac{3^{6}}{2^{5}}\times \left(\frac{2}{3}\right)^{5}$$

Cancel out 117649 in both numerator and denominator.

$$\frac{78125}{15625}-\frac{3^{6}}{2^{5}}\times \left(\frac{2}{3}\right)^{5}$$

Divide 78125 by 15625 to get 5.

$$5-\frac{3^{6}}{2^{5}}\times \left(\frac{2}{3}\right)^{5}$$

Calculate 3 to the power of 6 and get 729.

$$5-\frac{729}{2^{5}}\times \left(\frac{2}{3}\right)^{5}$$

Calculate 2 to the power of 5 and get 32.

$$5-\frac{729}{32}\times \left(\frac{2}{3}\right)^{5}$$

Calculate \frac{2}{3} to the power of 5 and get \frac{32}{243}.

$$5-\frac{729}{32}\times \frac{32}{243}$$

Multiply \frac{729}{32} times \frac{32}{243} by multiplying numerator times numerator and denominator times denominator.

$$5-\frac{729\times 32}{32\times 243}$$

Cancel out 32 in both numerator and denominator.

$$5-\frac{729}{243}$$

Divide 729 by 243 to get 3.

$$5-3$$

Subtract 3 from 5 to get 2.

$$2$$

Factor

$$2$$