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

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

Evaluate

$$-3z^{3}x^{9}y^{10}$$

Solution Steps

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

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

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

$$\left(-x^{2}\right)^{3}y^{9}\times 3x^{3}yz^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$\left(-x^{2}\right)^{3}y^{10}\times 3x^{3}z^{3}$$

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

$$\left(-1\right)^{3}\left(x^{2}\right)^{3}y^{10}\times 3x^{3}z^{3}$$

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

$$\left(-1\right)^{3}x^{6}y^{10}\times 3x^{3}z^{3}$$

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

$$-x^{6}y^{10}\times 3x^{3}z^{3}$$

Multiply -1 and 3 to get -3.

$$-3x^{6}y^{10}x^{3}z^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-3x^{9}y^{10}z^{3}$$

Expand

$$-3z^{3}x^{9}y^{10}$$

Solution Steps

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

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

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

$$\left(-x^{2}\right)^{3}y^{9}\times 3x^{3}yz^{3}$$

To multiply powers of the same base, add their exponents. Add 9 and 1 to get 10.

$$\left(-x^{2}\right)^{3}y^{10}\times 3x^{3}z^{3}$$

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

$$\left(-1\right)^{3}\left(x^{2}\right)^{3}y^{10}\times 3x^{3}z^{3}$$

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

$$\left(-1\right)^{3}x^{6}y^{10}\times 3x^{3}z^{3}$$

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

$$-x^{6}y^{10}\times 3x^{3}z^{3}$$

Multiply -1 and 3 to get -3.

$$-3x^{6}y^{10}x^{3}z^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 3 to get 9.

$$-3x^{9}y^{10}z^{3}$$