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

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

Evaluate

$$27y^{2}z^{4}x^{13}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$\left(x^{2}\right)^{2}y^{2}z^{4}\times 3^{3}x^{9}$$

Calculate 3 to the power of 3 and get 27.

$$\left(x^{2}\right)^{2}y^{2}z^{4}\times 27x^{9}$$

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

$$x^{4}y^{2}z^{4}\times 27x^{9}$$

To multiply powers of the same base, add their exponents. Add 4 and 9 to get 13.

$$x^{13}y^{2}z^{4}\times 27$$

Expand

$$27y^{2}z^{4}x^{13}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$\left(x^{2}\right)^{2}y^{2}z^{4}\times 3^{3}x^{9}$$

Calculate 3 to the power of 3 and get 27.

$$\left(x^{2}\right)^{2}y^{2}z^{4}\times 27x^{9}$$

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

$$x^{4}y^{2}z^{4}\times 27x^{9}$$

To multiply powers of the same base, add their exponents. Add 4 and 9 to get 13.

$$x^{13}y^{2}z^{4}\times 27$$