Solve [x^{5}+(1/2x^{3}y)^{3}:(-1/8x^{4}y^3)]+3x^3*[y^4z:(-y^3z)]=

$$[ x ^ { 5 } + ( \frac { 1 } { 2 } x ^ { 3 } y ) ^ { 3 } : ( - \frac { 1 } { 8 } x ^ { 4 } y ^ { 3 } ) ] + 3 x ^ { 3 } \cdot [ y ^ { 4 } z : ( - y ^ { 3 } z ) ] =$$

Evaluate

$$-3yx^{3}$$

Solution Steps

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

$$x^{5}+\frac{\left(\frac{1}{2}\right)^{3}\left(x^{3}\right)^{3}y^{3}}{-\frac{1}{8}x^{4}y^{3}}+3x^{3}\times \frac{y^{4}z}{\left(-y^{3}\right)z}$$

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

$$x^{5}+\frac{\left(\frac{1}{2}\right)^{3}x^{9}y^{3}}{-\frac{1}{8}x^{4}y^{3}}+3x^{3}\times \frac{y^{4}z}{\left(-y^{3}\right)z}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$x^{5}+\frac{\frac{1}{8}x^{9}y^{3}}{-\frac{1}{8}x^{4}y^{3}}+3x^{3}\times \frac{y^{4}z}{\left(-y^{3}\right)z}$$

Cancel out y^{3}x^{4} in both numerator and denominator.

$$x^{5}+\frac{\frac{1}{8}x^{5}}{-\frac{1}{8}}+3x^{3}\times \frac{y^{4}z}{\left(-y^{3}\right)z}$$

Cancel out -\frac{1}{8} and -\frac{1}{8}.

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

Combine x^{5} and -x^{5} to get 0.

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

Cancel out z in both numerator and denominator.

$$3x^{3}\times \frac{y^{4}}{-y^{3}}$$

Express 3\times \frac{y^{4}}{-y^{3}} as a single fraction.

$$\frac{3y^{4}}{-y^{3}}x^{3}$$

Express \frac{3y^{4}}{-y^{3}}x^{3} as a single fraction.

$$\frac{3y^{4}x^{3}}{-y^{3}}$$

Cancel out y^{3} in both numerator and denominator.

$$\frac{3yx^{3}}{-1}$$

Anything divided by -1 gives its opposite.

$$-3yx^{3}$$

Expand

$$-3yx^{3}$$

Solution Steps

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

$$x^{5}+\frac{\left(\frac{1}{2}\right)^{3}\left(x^{3}\right)^{3}y^{3}}{-\frac{1}{8}x^{4}y^{3}}+3x^{3}\times \frac{y^{4}z}{\left(-y^{3}\right)z}$$

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

$$x^{5}+\frac{\left(\frac{1}{2}\right)^{3}x^{9}y^{3}}{-\frac{1}{8}x^{4}y^{3}}+3x^{3}\times \frac{y^{4}z}{\left(-y^{3}\right)z}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$x^{5}+\frac{\frac{1}{8}x^{9}y^{3}}{-\frac{1}{8}x^{4}y^{3}}+3x^{3}\times \frac{y^{4}z}{\left(-y^{3}\right)z}$$

Cancel out y^{3}x^{4} in both numerator and denominator.

$$x^{5}+\frac{\frac{1}{8}x^{5}}{-\frac{1}{8}}+3x^{3}\times \frac{y^{4}z}{\left(-y^{3}\right)z}$$

Cancel out -\frac{1}{8} and -\frac{1}{8}.

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

Combine x^{5} and -x^{5} to get 0.

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

Cancel out z in both numerator and denominator.

$$3x^{3}\times \frac{y^{4}}{-y^{3}}$$

Express 3\times \frac{y^{4}}{-y^{3}} as a single fraction.

$$\frac{3y^{4}}{-y^{3}}x^{3}$$

Express \frac{3y^{4}}{-y^{3}}x^{3} as a single fraction.

$$\frac{3y^{4}x^{3}}{-y^{3}}$$

Cancel out y^{3} in both numerator and denominator.

$$\frac{3yx^{3}}{-1}$$

Anything divided by -1 gives its opposite.

$$-3yx^{3}$$