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

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

Evaluate

$$3z^{2}x^{5}y^{11}$$

Solution Steps

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

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

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

$$\left(-x^{2}\right)^{2}y^{8}\times 3xy^{3}z^{2}$$

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

$$\left(x^{2}\right)^{2}y^{8}\times 3xy^{3}z^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$\left(x^{2}\right)^{2}y^{11}\times 3xz^{2}$$

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

$$x^{4}y^{11}\times 3xz^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$x^{5}y^{11}\times 3z^{2}$$

Expand

$$3z^{2}x^{5}y^{11}$$

Solution Steps

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

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

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

$$\left(-x^{2}\right)^{2}y^{8}\times 3xy^{3}z^{2}$$

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

$$\left(x^{2}\right)^{2}y^{8}\times 3xy^{3}z^{2}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$\left(x^{2}\right)^{2}y^{11}\times 3xz^{2}$$

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

$$x^{4}y^{11}\times 3xz^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$x^{5}y^{11}\times 3z^{2}$$