Solve 2(-(-x^{3})^{2}y^{7})^{4}(-(-2(-x^3y)^3)^5)^3=

$$2 ( - ( - x ^ { 3 } ) ^ { 2 } y ^ { 7 } ) ^ { 4 } ( - ( - 2 ( - x ^ { 3 } y ) ^ { 3 } ) ^ { 5 } ) ^ { 3 } =$$

Evaluate

$$-65536y^{73}x^{159}$$

Solution Steps

Calculate -x^{3} to the power of 2 and get \left(x^{3}\right)^{2}.

$$2\left(\left(-\left(x^{3}\right)^{2}\right)y^{7}\right)^{4}\left(-\left(-2\left(\left(-x^{3}\right)y\right)^{3}\right)^{5}\right)^{3}$$

Expand \left(\left(-\left(x^{3}\right)^{2}\right)y^{7}\right)^{4}.

$$2\left(-\left(x^{3}\right)^{2}\right)^{4}\left(y^{7}\right)^{4}\left(-\left(-2\left(\left(-x^{3}\right)y\right)^{3}\right)^{5}\right)^{3}$$

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

$$2\left(-x^{6}\right)^{4}\left(y^{7}\right)^{4}\left(-\left(-2\left(\left(-x^{3}\right)y\right)^{3}\right)^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-2\left(\left(-x^{3}\right)y\right)^{3}\right)^{5}\right)^{3}$$

Expand \left(\left(-x^{3}\right)y\right)^{3}.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-2\left(-x^{3}\right)^{3}y^{3}\right)^{5}\right)^{3}$$

Expand \left(-2\left(-x^{3}\right)^{3}y^{3}\right)^{5}.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-2\right)^{5}\left(\left(-x^{3}\right)^{3}\right)^{5}\left(y^{3}\right)^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-2\right)^{5}\left(-x^{3}\right)^{15}\left(y^{3}\right)^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-2\right)^{5}\left(-x^{3}\right)^{15}y^{15}\right)^{3}$$

Calculate -2 to the power of 5 and get -32.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-32\left(-x^{3}\right)^{15}y^{15}\right)\right)^{3}$$

The opposite of -32\left(-x^{3}\right)^{15}y^{15} is 32\left(-x^{3}\right)^{15}y^{15}.

$$2\left(-x^{6}\right)^{4}y^{28}\times \left(32\left(-x^{3}\right)^{15}y^{15}\right)^{3}$$

Expand \left(32\left(-x^{3}\right)^{15}y^{15}\right)^{3}.

$$2\left(-x^{6}\right)^{4}y^{28}\times 32^{3}\left(\left(-x^{3}\right)^{15}\right)^{3}\left(y^{15}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 15 and 3 to get 45.

$$2\left(-x^{6}\right)^{4}y^{28}\times 32^{3}\left(-x^{3}\right)^{45}\left(y^{15}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 15 and 3 to get 45.

$$2\left(-x^{6}\right)^{4}y^{28}\times 32^{3}\left(-x^{3}\right)^{45}y^{45}$$

Calculate 32 to the power of 3 and get 32768.

$$2\left(-x^{6}\right)^{4}y^{28}\times 32768\left(-x^{3}\right)^{45}y^{45}$$

Multiply 2 and 32768 to get 65536.

$$65536\left(-x^{6}\right)^{4}y^{28}\left(-x^{3}\right)^{45}y^{45}$$

To multiply powers of the same base, add their exponents. Add 28 and 45 to get 73.

$$65536\left(-x^{6}\right)^{4}y^{73}\left(-x^{3}\right)^{45}$$

Expand \left(-x^{6}\right)^{4}.

$$65536\left(-1\right)^{4}\left(x^{6}\right)^{4}y^{73}\left(-x^{3}\right)^{45}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 4 to get 24.

$$65536\left(-1\right)^{4}x^{24}y^{73}\left(-x^{3}\right)^{45}$$

Calculate -1 to the power of 4 and get 1.

$$65536\times 1x^{24}y^{73}\left(-x^{3}\right)^{45}$$

Multiply 65536 and 1 to get 65536.

$$65536x^{24}y^{73}\left(-x^{3}\right)^{45}$$

Expand \left(-x^{3}\right)^{45}.

$$65536x^{24}y^{73}\left(-1\right)^{45}\left(x^{3}\right)^{45}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 45 to get 135.

$$65536x^{24}y^{73}\left(-1\right)^{45}x^{135}$$

Calculate -1 to the power of 45 and get -1.

$$65536x^{24}y^{73}\left(-1\right)x^{135}$$

Multiply 65536 and -1 to get -65536.

$$-65536x^{24}y^{73}x^{135}$$

To multiply powers of the same base, add their exponents. Add 24 and 135 to get 159.

$$-65536x^{159}y^{73}$$

Expand

$$-65536y^{73}x^{159}$$

Solution Steps

Calculate -x^{3} to the power of 2 and get \left(x^{3}\right)^{2}.

$$2\left(\left(-\left(x^{3}\right)^{2}\right)y^{7}\right)^{4}\left(-\left(-2\left(\left(-x^{3}\right)y\right)^{3}\right)^{5}\right)^{3}$$

Expand \left(\left(-\left(x^{3}\right)^{2}\right)y^{7}\right)^{4}.

$$2\left(-\left(x^{3}\right)^{2}\right)^{4}\left(y^{7}\right)^{4}\left(-\left(-2\left(\left(-x^{3}\right)y\right)^{3}\right)^{5}\right)^{3}$$

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

$$2\left(-x^{6}\right)^{4}\left(y^{7}\right)^{4}\left(-\left(-2\left(\left(-x^{3}\right)y\right)^{3}\right)^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-2\left(\left(-x^{3}\right)y\right)^{3}\right)^{5}\right)^{3}$$

Expand \left(\left(-x^{3}\right)y\right)^{3}.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-2\left(-x^{3}\right)^{3}y^{3}\right)^{5}\right)^{3}$$

Expand \left(-2\left(-x^{3}\right)^{3}y^{3}\right)^{5}.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-2\right)^{5}\left(\left(-x^{3}\right)^{3}\right)^{5}\left(y^{3}\right)^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-2\right)^{5}\left(-x^{3}\right)^{15}\left(y^{3}\right)^{5}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-2\right)^{5}\left(-x^{3}\right)^{15}y^{15}\right)^{3}$$

Calculate -2 to the power of 5 and get -32.

$$2\left(-x^{6}\right)^{4}y^{28}\left(-\left(-32\left(-x^{3}\right)^{15}y^{15}\right)\right)^{3}$$

The opposite of -32\left(-x^{3}\right)^{15}y^{15} is 32\left(-x^{3}\right)^{15}y^{15}.

$$2\left(-x^{6}\right)^{4}y^{28}\times \left(32\left(-x^{3}\right)^{15}y^{15}\right)^{3}$$

Expand \left(32\left(-x^{3}\right)^{15}y^{15}\right)^{3}.

$$2\left(-x^{6}\right)^{4}y^{28}\times 32^{3}\left(\left(-x^{3}\right)^{15}\right)^{3}\left(y^{15}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 15 and 3 to get 45.

$$2\left(-x^{6}\right)^{4}y^{28}\times 32^{3}\left(-x^{3}\right)^{45}\left(y^{15}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 15 and 3 to get 45.

$$2\left(-x^{6}\right)^{4}y^{28}\times 32^{3}\left(-x^{3}\right)^{45}y^{45}$$

Calculate 32 to the power of 3 and get 32768.

$$2\left(-x^{6}\right)^{4}y^{28}\times 32768\left(-x^{3}\right)^{45}y^{45}$$

Multiply 2 and 32768 to get 65536.

$$65536\left(-x^{6}\right)^{4}y^{28}\left(-x^{3}\right)^{45}y^{45}$$

To multiply powers of the same base, add their exponents. Add 28 and 45 to get 73.

$$65536\left(-x^{6}\right)^{4}y^{73}\left(-x^{3}\right)^{45}$$

Expand \left(-x^{6}\right)^{4}.

$$65536\left(-1\right)^{4}\left(x^{6}\right)^{4}y^{73}\left(-x^{3}\right)^{45}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 4 to get 24.

$$65536\left(-1\right)^{4}x^{24}y^{73}\left(-x^{3}\right)^{45}$$

Calculate -1 to the power of 4 and get 1.

$$65536\times 1x^{24}y^{73}\left(-x^{3}\right)^{45}$$

Multiply 65536 and 1 to get 65536.

$$65536x^{24}y^{73}\left(-x^{3}\right)^{45}$$

Expand \left(-x^{3}\right)^{45}.

$$65536x^{24}y^{73}\left(-1\right)^{45}\left(x^{3}\right)^{45}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 45 to get 135.

$$65536x^{24}y^{73}\left(-1\right)^{45}x^{135}$$

Calculate -1 to the power of 45 and get -1.

$$65536x^{24}y^{73}\left(-1\right)x^{135}$$

Multiply 65536 and -1 to get -65536.

$$-65536x^{24}y^{73}x^{135}$$

To multiply powers of the same base, add their exponents. Add 24 and 135 to get 159.

$$-65536x^{159}y^{73}$$