Solve [(-2x^{2})^{3}(-xy^{4})^{2}]^{2}div[-(-x^{2}y)^2(-xy^2)^3]^3

$$[ ( - 2 x ^ { 2 } ) ^ { 3 } ( - x y ^ { 4 } ) ^ { 2 } ] ^ { 2 } \div [ - ( - x ^ { 2 } y ) ^ { 2 } ( - x y ^ { 2 } ) ^ { 3 } ] ^ { 3 }$$

Evaluate

$$\frac{64}{x^{5}y^{8}}$$

Short Solution Steps

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$\frac{\left(-8x^{6}\left(\left(-x\right)y^{4}\right)^{2}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{\left(-8x^{6}\left(-x\right)^{2}\left(y^{4}\right)^{2}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(-8x^{6}\left(-x\right)^{2}y^{8}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

Calculate -x to the power of 2 and get x^{2}.

$$\frac{\left(-8x^{6}x^{2}y^{8}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{\left(-8x^{8}y^{8}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

Expand \left(-8x^{8}y^{8}\right)^{2}.

$$\frac{\left(-8\right)^{2}\left(x^{8}\right)^{2}\left(y^{8}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{\left(-8\right)^{2}x^{16}\left(y^{8}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{\left(-8\right)^{2}x^{16}y^{16}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

Calculate -8 to the power of 2 and get 64.

$$\frac{64x^{16}y^{16}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{64x^{16}y^{16}}{\left(\left(-\left(-x^{2}\right)^{2}y^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{64x^{16}y^{16}}{\left(\left(-\left(x^{2}\right)^{2}y^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{64x^{16}y^{16}}{\left(\left(-\left(x^{2}\right)^{2}y^{2}\right)\left(-x\right)^{3}\left(y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{64x^{16}y^{16}}{\left(\left(-\left(x^{2}\right)^{2}y^{2}\right)\left(-x\right)^{3}y^{6}\right)^{3}}$$

Expand \left(\left(-\left(x^{2}\right)^{2}y^{2}\right)\left(-x\right)^{3}y^{6}\right)^{3}.

$$\frac{64x^{16}y^{16}}{\left(-\left(x^{2}\right)^{2}y^{2}\right)^{3}\left(\left(-x\right)^{3}\right)^{3}\left(y^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{64x^{16}y^{16}}{\left(-x^{4}y^{2}\right)^{3}\left(\left(-x\right)^{3}\right)^{3}\left(y^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{64x^{16}y^{16}}{\left(-x^{4}y^{2}\right)^{3}\left(-x\right)^{9}\left(y^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{64x^{16}y^{16}}{\left(-x^{4}y^{2}\right)^{3}\left(-x\right)^{9}y^{18}}$$

Cancel out y^{16} in both numerator and denominator.

$$\frac{64x^{16}}{y^{2}\left(-x\right)^{9}\left(-y^{2}x^{4}\right)^{3}}$$

Expand \left(-x\right)^{9}.

$$\frac{64x^{16}}{y^{2}\left(-1\right)^{9}x^{9}\left(-y^{2}x^{4}\right)^{3}}$$

Calculate -1 to the power of 9 and get -1.

$$\frac{64x^{16}}{y^{2}\left(-1\right)x^{9}\left(-y^{2}x^{4}\right)^{3}}$$

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

$$\frac{64x^{16}}{y^{2}\left(-1\right)x^{9}\left(-1\right)^{3}\left(y^{2}\right)^{3}\left(x^{4}\right)^{3}}$$

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

$$\frac{64x^{16}}{y^{2}\left(-1\right)x^{9}\left(-1\right)^{3}y^{6}\left(x^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{64x^{16}}{y^{2}\left(-1\right)x^{9}\left(-1\right)^{3}y^{6}x^{12}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{64x^{16}}{y^{2}\left(-1\right)x^{9}\left(-1\right)y^{6}x^{12}}$$

Multiply -1 and -1 to get 1.

$$\frac{64x^{16}}{y^{2}x^{9}y^{6}x^{12}}$$

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

$$\frac{64x^{16}}{y^{8}x^{9}x^{12}}$$

To multiply powers of the same base, add their exponents. Add 9 and 12 to get 21.

$$\frac{64x^{16}}{y^{8}x^{21}}$$

Cancel out x^{16} in both numerator and denominator.

$$\frac{64}{x^{5}y^{8}}$$

Expand

$$\frac{64}{x^{5}y^{8}}$$

Short Solution Steps

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

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

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

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

Calculate -2 to the power of 3 and get -8.

$$\frac{\left(-8x^{6}\left(\left(-x\right)y^{4}\right)^{2}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{\left(-8x^{6}\left(-x\right)^{2}\left(y^{4}\right)^{2}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(-8x^{6}\left(-x\right)^{2}y^{8}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

Calculate -x to the power of 2 and get x^{2}.

$$\frac{\left(-8x^{6}x^{2}y^{8}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{\left(-8x^{8}y^{8}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

Expand \left(-8x^{8}y^{8}\right)^{2}.

$$\frac{\left(-8\right)^{2}\left(x^{8}\right)^{2}\left(y^{8}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{\left(-8\right)^{2}x^{16}\left(y^{8}\right)^{2}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$\frac{\left(-8\right)^{2}x^{16}y^{16}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

Calculate -8 to the power of 2 and get 64.

$$\frac{64x^{16}y^{16}}{\left(\left(-\left(\left(-x^{2}\right)y\right)^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{64x^{16}y^{16}}{\left(\left(-\left(-x^{2}\right)^{2}y^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{64x^{16}y^{16}}{\left(\left(-\left(x^{2}\right)^{2}y^{2}\right)\left(\left(-x\right)y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{64x^{16}y^{16}}{\left(\left(-\left(x^{2}\right)^{2}y^{2}\right)\left(-x\right)^{3}\left(y^{2}\right)^{3}\right)^{3}}$$

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

$$\frac{64x^{16}y^{16}}{\left(\left(-\left(x^{2}\right)^{2}y^{2}\right)\left(-x\right)^{3}y^{6}\right)^{3}}$$

Expand \left(\left(-\left(x^{2}\right)^{2}y^{2}\right)\left(-x\right)^{3}y^{6}\right)^{3}.

$$\frac{64x^{16}y^{16}}{\left(-\left(x^{2}\right)^{2}y^{2}\right)^{3}\left(\left(-x\right)^{3}\right)^{3}\left(y^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{64x^{16}y^{16}}{\left(-x^{4}y^{2}\right)^{3}\left(\left(-x\right)^{3}\right)^{3}\left(y^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{64x^{16}y^{16}}{\left(-x^{4}y^{2}\right)^{3}\left(-x\right)^{9}\left(y^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{64x^{16}y^{16}}{\left(-x^{4}y^{2}\right)^{3}\left(-x\right)^{9}y^{18}}$$

Cancel out y^{16} in both numerator and denominator.

$$\frac{64x^{16}}{y^{2}\left(-x\right)^{9}\left(-y^{2}x^{4}\right)^{3}}$$

Expand \left(-x\right)^{9}.

$$\frac{64x^{16}}{y^{2}\left(-1\right)^{9}x^{9}\left(-y^{2}x^{4}\right)^{3}}$$

Calculate -1 to the power of 9 and get -1.

$$\frac{64x^{16}}{y^{2}\left(-1\right)x^{9}\left(-y^{2}x^{4}\right)^{3}}$$

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

$$\frac{64x^{16}}{y^{2}\left(-1\right)x^{9}\left(-1\right)^{3}\left(y^{2}\right)^{3}\left(x^{4}\right)^{3}}$$

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

$$\frac{64x^{16}}{y^{2}\left(-1\right)x^{9}\left(-1\right)^{3}y^{6}\left(x^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{64x^{16}}{y^{2}\left(-1\right)x^{9}\left(-1\right)^{3}y^{6}x^{12}}$$

Calculate -1 to the power of 3 and get -1.

$$\frac{64x^{16}}{y^{2}\left(-1\right)x^{9}\left(-1\right)y^{6}x^{12}}$$

Multiply -1 and -1 to get 1.

$$\frac{64x^{16}}{y^{2}x^{9}y^{6}x^{12}}$$

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

$$\frac{64x^{16}}{y^{8}x^{9}x^{12}}$$

To multiply powers of the same base, add their exponents. Add 9 and 12 to get 21.

$$\frac{64x^{16}}{y^{8}x^{21}}$$

Cancel out x^{16} in both numerator and denominator.

$$\frac{64}{x^{5}y^{8}}$$