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

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

Evaluate

$$8y^{9}x^{16}$$

Solution Steps

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

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

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

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

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

$$\left(-x^{2}\right)^{5}\left(-2\right)^{3}x^{6}y^{9}$$

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

$$\left(-x^{2}\right)^{5}\left(-8\right)x^{6}y^{9}$$

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

$$\left(-1\right)^{5}\left(x^{2}\right)^{5}\left(-8\right)x^{6}y^{9}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\left(-1\right)^{5}x^{10}\left(-8\right)x^{6}y^{9}$$

Calculate -1 to the power of 5 and get -1.

$$-x^{10}\left(-8\right)x^{6}y^{9}$$

Multiply -1 and -8 to get 8.

$$8x^{10}x^{6}y^{9}$$

To multiply powers of the same base, add their exponents. Add 10 and 6 to get 16.

$$8x^{16}y^{9}$$

Expand

$$8y^{9}x^{16}$$

Solution Steps

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

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

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

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

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

$$\left(-x^{2}\right)^{5}\left(-2\right)^{3}x^{6}y^{9}$$

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

$$\left(-x^{2}\right)^{5}\left(-8\right)x^{6}y^{9}$$

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

$$\left(-1\right)^{5}\left(x^{2}\right)^{5}\left(-8\right)x^{6}y^{9}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\left(-1\right)^{5}x^{10}\left(-8\right)x^{6}y^{9}$$

Calculate -1 to the power of 5 and get -1.

$$-x^{10}\left(-8\right)x^{6}y^{9}$$

Multiply -1 and -8 to get 8.

$$8x^{10}x^{6}y^{9}$$

To multiply powers of the same base, add their exponents. Add 10 and 6 to get 16.

$$8x^{16}y^{9}$$