Solve {left({left({left(left(left(1^1right)^1right)^1frac{1/1right)}^{3}1/1right)}^{3}}{1}right)}^{2}={left({left(frac{{left(frac{{left({left(1frac{1/1right)}^{3}1/1frac{1}{1}right)}^2}{1}right)}^2}{1}right)}^2}{1}right)}^2

$${ \left( \frac{ { \left( { \left( { \left( { \left( { 1 }^{ 1 } \right) }^{ 1 } \right) }^{ 1 } \frac { 1 } { 1 } \right) }^{ 3 } \frac { 1 } { 1 } \right) }^{ 3 } }{ 1 } \right) }^{ 2 } = { \left( \frac{ { \left( \frac{ { \left( \frac{ { \left( { \left( 1 \frac { 1 } { 1 } \right) }^{ 3 } \frac { 1 } { 1 } \frac { 1 } { 1 } \right) }^{ 2 } }{ 1 } \right) }^{ 2 } }{ 1 } \right) }^{ 2 } }{ 1 } \right) }^{ 2 }$$

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Solution Steps

To raise a power to another power, multiply the exponents. Multiply 1 and 1 to get 1.

$$\left(\frac{\left(\left(\left(1^{1}\right)^{1}\times \frac{1}{1}\right)^{3}\times \frac{1}{1}\right)^{3}}{1}\right)^{2}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times \frac{1}{1}\times \frac{1}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 1 and 1 to get 1.

$$\left(\frac{\left(\left(1^{1}\times \frac{1}{1}\right)^{3}\times \frac{1}{1}\right)^{3}}{1}\right)^{2}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times \frac{1}{1}\times \frac{1}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Divide 1 by 1 to get 1.

$$\left(\frac{\left(\left(1^{1}\times 1\right)^{3}\times \frac{1}{1}\right)^{3}}{1}\right)^{2}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times \frac{1}{1}\times \frac{1}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 1 to get 2.

$$\left(\frac{\left(\left(1^{2}\right)^{3}\times \frac{1}{1}\right)^{3}}{1}\right)^{2}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times \frac{1}{1}\times \frac{1}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(\frac{\left(1^{6}\times \frac{1}{1}\right)^{3}}{1}\right)^{2}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times \frac{1}{1}\times \frac{1}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Divide 1 by 1 to get 1.

$$\left(\frac{\left(1^{6}\times 1\right)^{3}}{1}\right)^{2}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times \frac{1}{1}\times \frac{1}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\left(\frac{\left(1^{7}\right)^{3}}{1}\right)^{2}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times \frac{1}{1}\times \frac{1}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\left(\frac{1^{21}}{1}\right)^{2}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times \frac{1}{1}\times \frac{1}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 21 to get 20.

$$\left(1^{20}\right)^{2}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times \frac{1}{1}\times \frac{1}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 20 and 2 to get 40.

$$1^{40}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times \frac{1}{1}\times \frac{1}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Divide 1 by 1 to get 1.

$$1^{40}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times 1\times \frac{1}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Divide 1 by 1 to get 1.

$$1^{40}=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times 1\times 1\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Calculate 1 to the power of 40 and get 1.

$$1=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1\times 1+1}{1}\right)^{3}\times 1\times 1\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Multiply 1 and 1 to get 1.

$$1=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{1+1}{1}\right)^{3}\times 1\times 1\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Add 1 and 1 to get 2.

$$1=\left(\frac{\left(\frac{\left(\frac{\left(\left(\frac{2}{1}\right)^{3}\times 1\times 1\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Anything divided by one gives itself.

$$1=\left(\frac{\left(\frac{\left(\frac{\left(2^{3}\times 1\times 1\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$1=\left(\frac{\left(\frac{\left(\frac{\left(8\times 1\times 1\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Multiply 8 and 1 to get 8.

$$1=\left(\frac{\left(\frac{\left(\frac{\left(8\times 1\right)^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Multiply 8 and 1 to get 8.

$$1=\left(\frac{\left(\frac{\left(\frac{8^{2}}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Calculate 8 to the power of 2 and get 64.

$$1=\left(\frac{\left(\frac{\left(\frac{64}{1}\right)^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Anything divided by one gives itself.

$$1=\left(\frac{\left(\frac{64^{2}}{1}\right)^{2}}{1}\right)^{2}$$

Calculate 64 to the power of 2 and get 4096.

$$1=\left(\frac{\left(\frac{4096}{1}\right)^{2}}{1}\right)^{2}$$

Anything divided by one gives itself.

$$1=\left(\frac{4096^{2}}{1}\right)^{2}$$

Calculate 4096 to the power of 2 and get 16777216.

$$1=\left(\frac{16777216}{1}\right)^{2}$$

Anything divided by one gives itself.

$$1=16777216^{2}$$

Calculate 16777216 to the power of 2 and get 281474976710656.

$$1=281474976710656$$

Compare 1 and 281474976710656.

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