Solve 6^26^26^26^2{6}^{2}{6}^{2}{6}^{2}{6}^{2}{6}^{2}{6}^2{6}^2{left({6}^2right)}^26

$${ 6 }^{ 2 } { 6 }^{ 2 } { 6 }^{ 2 } { 6 }^{ 2 } { 6 }^{ 2 } { 6 }^{ 2 } { 6 }^{ 2 } { 6 }^{ 2 } { 6 }^{ 2 } { 6 }^{ 2 } { 6 }^{ 2 } { \left( { 6 }^{ 2 } \right) }^{ 26 }$$

Evaluate

$$3829944921253794893077685127088430174646042802674934480896$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 26 to get 52.

$$6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{52}$$

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$6^{4}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{52}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$6^{6}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{52}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$6^{8}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{52}$$

To multiply powers of the same base, add their exponents. Add 8 and 2 to get 10.

$$6^{10}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{52}$$

To multiply powers of the same base, add their exponents. Add 10 and 2 to get 12.

$$6^{12}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{52}$$

To multiply powers of the same base, add their exponents. Add 12 and 2 to get 14.

$$6^{14}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{52}$$

To multiply powers of the same base, add their exponents. Add 14 and 2 to get 16.

$$6^{16}\times 6^{2}\times 6^{2}\times 6^{2}\times 6^{52}$$

To multiply powers of the same base, add their exponents. Add 16 and 2 to get 18.

$$6^{18}\times 6^{2}\times 6^{2}\times 6^{52}$$

To multiply powers of the same base, add their exponents. Add 18 and 2 to get 20.

$$6^{20}\times 6^{2}\times 6^{52}$$

To multiply powers of the same base, add their exponents. Add 20 and 2 to get 22.

$$6^{22}\times 6^{52}$$

To multiply powers of the same base, add their exponents. Add 22 and 52 to get 74.

$$6^{74}$$

Calculate 6 to the power of 74 and get 3829944921253794893077685127088430174646042802674934480896.

$$3829944921253794893077685127088430174646042802674934480896$$

Factor

$$2^{74}\times 3^{74}$$