Solve 2^22^22^22^2{2}^2{2}^2{2}^2{2}^

$${ 2 }^{ 2 } { 2 }^{ 2 } { 2 }^{ 2 } { 2 }^{ 2 } { 2 }^{ 2 } { 2 }^{ 2 } { 2 }^{ 2 } { 2 }^{ }$$

Evaluate

$$32768$$

Solution Steps

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

$$2^{4}\times 2^{2}\times 2^{2}\times 2^{2}\times 2^{2}\times 2^{2}\times 2^{1}$$

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

$$2^{6}\times 2^{2}\times 2^{2}\times 2^{2}\times 2^{2}\times 2^{1}$$

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

$$2^{8}\times 2^{2}\times 2^{2}\times 2^{2}\times 2^{1}$$

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

$$2^{10}\times 2^{2}\times 2^{2}\times 2^{1}$$

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

$$2^{12}\times 2^{2}\times 2^{1}$$

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

$$2^{14}\times 2^{1}$$

To multiply powers of the same base, add their exponents. Add 14 and 1 to get 15.

$$2^{15}$$

Calculate 2 to the power of 15 and get 32768.

$$32768$$

Factor

$$2^{15}$$