Solve 18x^{3}yz*(-1/3y^2z)^3div1/6x^2y^2z

$$18 x ^ { 3 } y z \cdot ( - \frac { 1 } { 3 } y ^ { 2 } z ) ^ { 3 } \div \frac { 1 } { 6 } x ^ { 2 } y ^ { 2 } z$$

Evaluate

$$-4y^{9}\left(xz\right)^{5}$$

Solution Steps

Expand \left(-\frac{1}{3}y^{2}z\right)^{3}.

$$\frac{18x^{3}yz\left(-\frac{1}{3}\right)^{3}\left(y^{2}\right)^{3}z^{3}}{\frac{1}{6}}x^{2}y^{2}z$$

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

$$\frac{18x^{3}yz\left(-\frac{1}{3}\right)^{3}y^{6}z^{3}}{\frac{1}{6}}x^{2}y^{2}z$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$\frac{18x^{3}yz\left(-\frac{1}{27}\right)y^{6}z^{3}}{\frac{1}{6}}x^{2}y^{2}z$$

Multiply 18 and -\frac{1}{27} to get -\frac{2}{3}.

$$\frac{-\frac{2}{3}x^{3}yzy^{6}z^{3}}{\frac{1}{6}}x^{2}y^{2}z$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{-\frac{2}{3}x^{3}y^{7}zz^{3}}{\frac{1}{6}}x^{2}y^{2}z$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{-\frac{2}{3}x^{3}y^{7}z^{4}}{\frac{1}{6}}x^{2}y^{2}z$$

Divide -\frac{2}{3}x^{3}y^{7}z^{4} by \frac{1}{6} by multiplying -\frac{2}{3}x^{3}y^{7}z^{4} by the reciprocal of \frac{1}{6}.

$$-\frac{2}{3}x^{3}y^{7}z^{4}\times 6x^{2}y^{2}z$$

Multiply -\frac{2}{3} and 6 to get -4.

$$-4x^{3}y^{7}z^{4}x^{2}y^{2}z$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-4x^{5}y^{7}z^{4}y^{2}z$$

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$-4x^{5}y^{9}z^{4}z$$

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

$$-4x^{5}y^{9}z^{5}$$

Expand

$$-4y^{9}\left(xz\right)^{5}$$

Solution Steps

Expand \left(-\frac{1}{3}y^{2}z\right)^{3}.

$$\frac{18x^{3}yz\left(-\frac{1}{3}\right)^{3}\left(y^{2}\right)^{3}z^{3}}{\frac{1}{6}}x^{2}y^{2}z$$

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

$$\frac{18x^{3}yz\left(-\frac{1}{3}\right)^{3}y^{6}z^{3}}{\frac{1}{6}}x^{2}y^{2}z$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$\frac{18x^{3}yz\left(-\frac{1}{27}\right)y^{6}z^{3}}{\frac{1}{6}}x^{2}y^{2}z$$

Multiply 18 and -\frac{1}{27} to get -\frac{2}{3}.

$$\frac{-\frac{2}{3}x^{3}yzy^{6}z^{3}}{\frac{1}{6}}x^{2}y^{2}z$$

To multiply powers of the same base, add their exponents. Add 1 and 6 to get 7.

$$\frac{-\frac{2}{3}x^{3}y^{7}zz^{3}}{\frac{1}{6}}x^{2}y^{2}z$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{-\frac{2}{3}x^{3}y^{7}z^{4}}{\frac{1}{6}}x^{2}y^{2}z$$

Divide -\frac{2}{3}x^{3}y^{7}z^{4} by \frac{1}{6} by multiplying -\frac{2}{3}x^{3}y^{7}z^{4} by the reciprocal of \frac{1}{6}.

$$-\frac{2}{3}x^{3}y^{7}z^{4}\times 6x^{2}y^{2}z$$

Multiply -\frac{2}{3} and 6 to get -4.

$$-4x^{3}y^{7}z^{4}x^{2}y^{2}z$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$-4x^{5}y^{7}z^{4}y^{2}z$$

To multiply powers of the same base, add their exponents. Add 7 and 2 to get 9.

$$-4x^{5}y^{9}z^{4}z$$

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

$$-4x^{5}y^{9}z^{5}$$