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

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

Evaluate

$$-243x^{2}\left(yz\right)^{13}$$

Solution Steps

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

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

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

$$\left(-3\right)^{3}y^{9}\left(z^{3}\right)^{3}\left(-3xy^{2}z^{2}\right)^{2}$$

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

$$\left(-3\right)^{3}y^{9}z^{9}\left(-3xy^{2}z^{2}\right)^{2}$$

Calculate -3 to the power of 3 and get -27.

$$-27y^{9}z^{9}\left(-3xy^{2}z^{2}\right)^{2}$$

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

$$-27y^{9}z^{9}\left(-3\right)^{2}x^{2}\left(y^{2}\right)^{2}\left(z^{2}\right)^{2}$$

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

$$-27y^{9}z^{9}\left(-3\right)^{2}x^{2}y^{4}\left(z^{2}\right)^{2}$$

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

$$-27y^{9}z^{9}\left(-3\right)^{2}x^{2}y^{4}z^{4}$$

Calculate -3 to the power of 2 and get 9.

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

Multiply -27 and 9 to get -243.

$$-243y^{9}z^{9}x^{2}y^{4}z^{4}$$

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

$$-243y^{13}z^{9}x^{2}z^{4}$$

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

$$-243y^{13}z^{13}x^{2}$$

Expand

$$-243x^{2}\left(yz\right)^{13}$$

Solution Steps

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

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

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

$$\left(-3\right)^{3}y^{9}\left(z^{3}\right)^{3}\left(-3xy^{2}z^{2}\right)^{2}$$

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

$$\left(-3\right)^{3}y^{9}z^{9}\left(-3xy^{2}z^{2}\right)^{2}$$

Calculate -3 to the power of 3 and get -27.

$$-27y^{9}z^{9}\left(-3xy^{2}z^{2}\right)^{2}$$

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

$$-27y^{9}z^{9}\left(-3\right)^{2}x^{2}\left(y^{2}\right)^{2}\left(z^{2}\right)^{2}$$

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

$$-27y^{9}z^{9}\left(-3\right)^{2}x^{2}y^{4}\left(z^{2}\right)^{2}$$

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

$$-27y^{9}z^{9}\left(-3\right)^{2}x^{2}y^{4}z^{4}$$

Calculate -3 to the power of 2 and get 9.

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

Multiply -27 and 9 to get -243.

$$-243y^{9}z^{9}x^{2}y^{4}z^{4}$$

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

$$-243y^{13}z^{9}x^{2}z^{4}$$

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

$$-243y^{13}z^{13}x^{2}$$