Solve left(6^5/6^3-left(3*5+2^23-2^4right)*left({2}^{2}{5}^{2}-{3}^4-{4}^2right)-frac{{2}^5}{{2}^4}right)*2

$$\left( \frac{ { 6 }^{ 5 } }{ { 6 }^{ 3 } } - \left( 3 \cdot 5+ { 2 }^{ 2 } 3- { 2 }^{ 4 } \right) \times \left( { 2 }^{ 2 } { 5 }^{ 2 } - { 3 }^{ 4 } - { 4 }^{ 2 } \right) - \frac{ { 2 }^{ 5 } }{ { 2 }^{ 4 } } \right) \times 2$$

Evaluate

$$2$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 5 to get 2.

$$\left(6^{2}-\left(3\times 5+2^{2}\times 3-2^{4}\right)\left(2^{2}\times 5^{2}-3^{4}-4^{2}\right)-\frac{2^{5}}{2^{4}}\right)\times 2$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$\left(6^{2}-\left(3\times 5+2^{2}\times 3-2^{4}\right)\left(2^{2}\times 5^{2}-3^{4}-4^{2}\right)-2^{1}\right)\times 2$$

Calculate 6 to the power of 2 and get 36.

$$\left(36-\left(3\times 5+2^{2}\times 3-2^{4}\right)\left(2^{2}\times 5^{2}-3^{4}-4^{2}\right)-2^{1}\right)\times 2$$

Multiply 3 and 5 to get 15.

$$\left(36-\left(15+2^{2}\times 3-2^{4}\right)\left(2^{2}\times 5^{2}-3^{4}-4^{2}\right)-2^{1}\right)\times 2$$

Calculate 2 to the power of 2 and get 4.

$$\left(36-\left(15+4\times 3-2^{4}\right)\left(2^{2}\times 5^{2}-3^{4}-4^{2}\right)-2^{1}\right)\times 2$$

Multiply 4 and 3 to get 12.

$$\left(36-\left(15+12-2^{4}\right)\left(2^{2}\times 5^{2}-3^{4}-4^{2}\right)-2^{1}\right)\times 2$$

Add 15 and 12 to get 27.

$$\left(36-\left(27-2^{4}\right)\left(2^{2}\times 5^{2}-3^{4}-4^{2}\right)-2^{1}\right)\times 2$$

Calculate 2 to the power of 4 and get 16.

$$\left(36-\left(27-16\right)\left(2^{2}\times 5^{2}-3^{4}-4^{2}\right)-2^{1}\right)\times 2$$

Subtract 16 from 27 to get 11.

$$\left(36-11\left(2^{2}\times 5^{2}-3^{4}-4^{2}\right)-2^{1}\right)\times 2$$

Calculate 2 to the power of 2 and get 4.

$$\left(36-11\left(4\times 5^{2}-3^{4}-4^{2}\right)-2^{1}\right)\times 2$$

Calculate 5 to the power of 2 and get 25.

$$\left(36-11\left(4\times 25-3^{4}-4^{2}\right)-2^{1}\right)\times 2$$

Multiply 4 and 25 to get 100.

$$\left(36-11\left(100-3^{4}-4^{2}\right)-2^{1}\right)\times 2$$

Calculate 3 to the power of 4 and get 81.

$$\left(36-11\left(100-81-4^{2}\right)-2^{1}\right)\times 2$$

Subtract 81 from 100 to get 19.

$$\left(36-11\left(19-4^{2}\right)-2^{1}\right)\times 2$$

Calculate 4 to the power of 2 and get 16.

$$\left(36-11\left(19-16\right)-2^{1}\right)\times 2$$

Subtract 16 from 19 to get 3.

$$\left(36-11\times 3-2^{1}\right)\times 2$$

Multiply 11 and 3 to get 33.

$$\left(36-33-2^{1}\right)\times 2$$

Subtract 33 from 36 to get 3.

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

Calculate 2 to the power of 1 and get 2.

$$\left(3-2\right)\times 2$$

Subtract 2 from 3 to get 1.

$$1\times 2$$

Multiply 1 and 2 to get 2.

$$2$$

Factor

$$2$$