Solve frac{(3^{5})^4*6^4}{9^7*4^2}

$$\frac { ( 3 ^ { 5 } ) ^ { 4 } \cdot 6 ^ { 4 } } { 9 ^ { 7 } \cdot 4 ^ { 2 } }$$

Evaluate

$$59049$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{3^{20}\times 6^{4}}{9^{7}\times 4^{2}}$$

Calculate 3 to the power of 20 and get 3486784401.

$$\frac{3486784401\times 6^{4}}{9^{7}\times 4^{2}}$$

Calculate 6 to the power of 4 and get 1296.

$$\frac{3486784401\times 1296}{9^{7}\times 4^{2}}$$

Multiply 3486784401 and 1296 to get 4518872583696.

$$\frac{4518872583696}{9^{7}\times 4^{2}}$$

Calculate 9 to the power of 7 and get 4782969.

$$\frac{4518872583696}{4782969\times 4^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{4518872583696}{4782969\times 16}$$

Multiply 4782969 and 16 to get 76527504.

$$\frac{4518872583696}{76527504}$$

Divide 4518872583696 by 76527504 to get 59049.

$$59049$$

Factor

$$3^{10}$$