Solve frac{27^{2}}{3^2}*25^3/5^9*(5/3)^4

$$\frac { 27 ^ { 2 } } { 3 ^ { 2 } } \times \frac { 25 ^ { 3 } } { 5 ^ { 9 } } \times ( \frac { 5 } { 3 } ) ^ { 4 }$$

Evaluate

$$5$$

Solution Steps

Calculate 27 to the power of 2 and get 729.

$$\frac{729}{3^{2}}\times \frac{25^{3}}{5^{9}}\times \left(\frac{5}{3}\right)^{4}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{729}{9}\times \frac{25^{3}}{5^{9}}\times \left(\frac{5}{3}\right)^{4}$$

Divide 729 by 9 to get 81.

$$81\times \frac{25^{3}}{5^{9}}\times \left(\frac{5}{3}\right)^{4}$$

Calculate 25 to the power of 3 and get 15625.

$$81\times \frac{15625}{5^{9}}\times \left(\frac{5}{3}\right)^{4}$$

Calculate 5 to the power of 9 and get 1953125.

$$81\times \frac{15625}{1953125}\times \left(\frac{5}{3}\right)^{4}$$

Reduce the fraction \frac{15625}{1953125} to lowest terms by extracting and canceling out 15625.

$$81\times \frac{1}{125}\times \left(\frac{5}{3}\right)^{4}$$

Multiply 81 and \frac{1}{125} to get \frac{81}{125}.

$$\frac{81}{125}\times \left(\frac{5}{3}\right)^{4}$$

Calculate \frac{5}{3} to the power of 4 and get \frac{625}{81}.

$$\frac{81}{125}\times \frac{625}{81}$$

Multiply \frac{81}{125} times \frac{625}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81\times 625}{125\times 81}$$

Cancel out 81 in both numerator and denominator.

$$\frac{625}{125}$$

Divide 625 by 125 to get 5.

$$5$$

Factor

$$5$$