Solve (-x^{3}y^{3})^2(x^2y^4z^2)

$$( - x ^ { 3 } y ^ { 3 } ) ^ { 2 } ( x ^ { 2 } y ^ { 4 } z ^ { 2 } )$$

Evaluate

$$z^{2}x^{8}y^{10}$$

Solution Steps

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

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

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

$$x^{6}y^{10}x^{2}z^{2}$$

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

$$x^{8}y^{10}z^{2}$$

Expand

$$z^{2}x^{8}y^{10}$$

Solution Steps

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

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

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

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

$$x^{6}y^{10}x^{2}z^{2}$$

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

$$x^{8}y^{10}z^{2}$$