Solve (-3xy)^{2}(-2/3x^2y)^3*(-3/4yz^2)^2

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

Evaluate

$$-\frac{3z^{4}y^{7}x^{8}}{2}$$

Solution Steps

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

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

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

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

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

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

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

$$9x^{2}y^{2}\left(-\frac{2}{3}\right)^{3}x^{6}y^{3}\left(-\frac{3}{4}yz^{2}\right)^{2}$$

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$9x^{2}y^{2}\left(-\frac{8}{27}\right)x^{6}y^{3}\left(-\frac{3}{4}yz^{2}\right)^{2}$$

Multiply 9 and -\frac{8}{27} to get -\frac{8}{3}.

$$-\frac{8}{3}x^{2}y^{2}x^{6}y^{3}\left(-\frac{3}{4}yz^{2}\right)^{2}$$

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

$$-\frac{8}{3}x^{8}y^{2}y^{3}\left(-\frac{3}{4}yz^{2}\right)^{2}$$

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

$$-\frac{8}{3}x^{8}y^{5}\left(-\frac{3}{4}yz^{2}\right)^{2}$$

Expand \left(-\frac{3}{4}yz^{2}\right)^{2}.

$$-\frac{8}{3}x^{8}y^{5}\left(-\frac{3}{4}\right)^{2}y^{2}\left(z^{2}\right)^{2}$$

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

$$-\frac{8}{3}x^{8}y^{5}\left(-\frac{3}{4}\right)^{2}y^{2}z^{4}$$

Calculate -\frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$-\frac{8}{3}x^{8}y^{5}\times \frac{9}{16}y^{2}z^{4}$$

Multiply -\frac{8}{3} and \frac{9}{16} to get -\frac{3}{2}.

$$-\frac{3}{2}x^{8}y^{5}y^{2}z^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$-\frac{3}{2}x^{8}y^{7}z^{4}$$

Expand

$$-\frac{3z^{4}y^{7}x^{8}}{2}$$

Solution Steps

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

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

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

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

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

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

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

$$9x^{2}y^{2}\left(-\frac{2}{3}\right)^{3}x^{6}y^{3}\left(-\frac{3}{4}yz^{2}\right)^{2}$$

Calculate -\frac{2}{3} to the power of 3 and get -\frac{8}{27}.

$$9x^{2}y^{2}\left(-\frac{8}{27}\right)x^{6}y^{3}\left(-\frac{3}{4}yz^{2}\right)^{2}$$

Multiply 9 and -\frac{8}{27} to get -\frac{8}{3}.

$$-\frac{8}{3}x^{2}y^{2}x^{6}y^{3}\left(-\frac{3}{4}yz^{2}\right)^{2}$$

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

$$-\frac{8}{3}x^{8}y^{2}y^{3}\left(-\frac{3}{4}yz^{2}\right)^{2}$$

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

$$-\frac{8}{3}x^{8}y^{5}\left(-\frac{3}{4}yz^{2}\right)^{2}$$

Expand \left(-\frac{3}{4}yz^{2}\right)^{2}.

$$-\frac{8}{3}x^{8}y^{5}\left(-\frac{3}{4}\right)^{2}y^{2}\left(z^{2}\right)^{2}$$

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

$$-\frac{8}{3}x^{8}y^{5}\left(-\frac{3}{4}\right)^{2}y^{2}z^{4}$$

Calculate -\frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$-\frac{8}{3}x^{8}y^{5}\times \frac{9}{16}y^{2}z^{4}$$

Multiply -\frac{8}{3} and \frac{9}{16} to get -\frac{3}{2}.

$$-\frac{3}{2}x^{8}y^{5}y^{2}z^{4}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$-\frac{3}{2}x^{8}y^{7}z^{4}$$