Solve {[(6^{7})^{2}*(6^{4})^{3}*(6^5)^4]*6^5}^3

$$\{ [ ( 6 ^ { 7 } ) ^ { 2 } \times ( 6 ^ { 4 } ) ^ { 3 } \cdot ( 6 ^ { 5 } ) ^ { 4 } ] \times 6 ^ { 5 } \} ^ { 3 }$$

Evaluate

$$114062085704338244191164816944498704846037491621658816825202465794722814645175316061268918687021135854361080842174857216$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\left(6^{14}\times \left(6^{4}\right)^{3}\times \left(6^{5}\right)^{4}\times 6^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\left(6^{14}\times 6^{12}\times \left(6^{5}\right)^{4}\times 6^{5}\right)^{3}$$

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

$$\left(6^{14}\times 6^{12}\times 6^{20}\times 6^{5}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 14 and 12 to get 26.

$$\left(6^{26}\times 6^{20}\times 6^{5}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 26 and 20 to get 46.

$$\left(6^{46}\times 6^{5}\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 46 and 5 to get 51.

$$\left(6^{51}\right)^{3}$$

Calculate 6 to the power of 51 and get 4849687664788584363858837602739217760256.

$$4849687664788584363858837602739217760256^{3}$$

Calculate 4849687664788584363858837602739217760256 to the power of 3 and get 114062085704338244191164816944498704846037491621658816825202465794722814645175316061268918687021135854361080842174857216.

$$114062085704338244191164816944498704846037491621658816825202465794722814645175316061268918687021135854361080842174857216$$

Factor

$$2^{153}\times 3^{153}$$