Solve 3^4*9^4/9^5:27^2:81

$$\frac { 3 ^ { 4 } \cdot 9 ^ { 4 } } { 9 ^ { 5 } : 27 ^ { 2 } } : 81$$

Evaluate

$$81$$

Solution Steps

Express \frac{\frac{3^{4}\times 9^{4}}{\frac{9^{5}}{27^{2}}}}{81} as a single fraction.

$$\frac{3^{4}\times 9^{4}}{\frac{9^{5}}{27^{2}}\times 81}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{81\times 9^{4}}{\frac{9^{5}}{27^{2}}\times 81}$$

Calculate 9 to the power of 4 and get 6561.

$$\frac{81\times 6561}{\frac{9^{5}}{27^{2}}\times 81}$$

Multiply 81 and 6561 to get 531441.

$$\frac{531441}{\frac{9^{5}}{27^{2}}\times 81}$$

Calculate 9 to the power of 5 and get 59049.

$$\frac{531441}{\frac{59049}{27^{2}}\times 81}$$

Calculate 27 to the power of 2 and get 729.

$$\frac{531441}{\frac{59049}{729}\times 81}$$

Divide 59049 by 729 to get 81.

$$\frac{531441}{81\times 81}$$

Multiply 81 and 81 to get 6561.

$$\frac{531441}{6561}$$

Divide 531441 by 6561 to get 81.

$$81$$

Factor

$$3^{4}$$