Solve (-3/4x^2yz^3)^2*(-8/9xy^4)

$$( - \frac { 3 } { 4 } x ^ { 2 } y z ^ { 3 } ) ^ { 2 } \cdot ( - \frac { 8 } { 9 } x y ^ { 4 } )$$

Evaluate

$$-\frac{x^{5}\left(yz\right)^{6}}{2}$$

Solution Steps

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

$$\left(-\frac{3}{4}\right)^{2}\left(x^{2}\right)^{2}y^{2}\left(z^{3}\right)^{2}\left(-\frac{8}{9}\right)xy^{4}$$

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

$$\left(-\frac{3}{4}\right)^{2}x^{4}y^{2}\left(z^{3}\right)^{2}\left(-\frac{8}{9}\right)xy^{4}$$

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

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

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

$$\frac{9}{16}x^{4}y^{2}z^{6}\left(-\frac{8}{9}\right)xy^{4}$$

Multiply \frac{9}{16} and -\frac{8}{9} to get -\frac{1}{2}.

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

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

$$-\frac{1}{2}x^{5}y^{2}z^{6}y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-\frac{1}{2}x^{5}y^{6}z^{6}$$

Expand

$$-\frac{x^{5}\left(yz\right)^{6}}{2}$$

Solution Steps

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

$$\left(-\frac{3}{4}\right)^{2}\left(x^{2}\right)^{2}y^{2}\left(z^{3}\right)^{2}\left(-\frac{8}{9}\right)xy^{4}$$

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

$$\left(-\frac{3}{4}\right)^{2}x^{4}y^{2}\left(z^{3}\right)^{2}\left(-\frac{8}{9}\right)xy^{4}$$

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

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

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

$$\frac{9}{16}x^{4}y^{2}z^{6}\left(-\frac{8}{9}\right)xy^{4}$$

Multiply \frac{9}{16} and -\frac{8}{9} to get -\frac{1}{2}.

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

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

$$-\frac{1}{2}x^{5}y^{2}z^{6}y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$-\frac{1}{2}x^{5}y^{6}z^{6}$$