Solve 2*z^2*(-z^3:z^2)^2=

$$2 \cdot z ^ { 2 } \cdot ( - z ^ { 3 } : z ^ { 2 } ) ^ { 2 } =$$

Evaluate

$$2z^{4}$$

Solution Steps

To raise \frac{-z^{3}}{z^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$2z^{2}\times \frac{\left(-z^{3}\right)^{2}}{\left(z^{2}\right)^{2}}$$

Express 2\times \frac{\left(-z^{3}\right)^{2}}{\left(z^{2}\right)^{2}} as a single fraction.

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

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

$$\frac{2\left(-z^{3}\right)^{2}}{z^{4}}z^{2}$$

Calculate -z^{3} to the power of 2 and get \left(z^{3}\right)^{2}.

$$\frac{2\left(z^{3}\right)^{2}}{z^{4}}z^{2}$$

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

$$\frac{2z^{6}}{z^{4}}z^{2}$$

Cancel out z^{4} in both numerator and denominator.

$$2z^{2}z^{2}$$

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

$$2z^{4}$$

Expand

$$2z^{4}$$

Solution Steps

To raise \frac{-z^{3}}{z^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$2z^{2}\times \frac{\left(-z^{3}\right)^{2}}{\left(z^{2}\right)^{2}}$$

Express 2\times \frac{\left(-z^{3}\right)^{2}}{\left(z^{2}\right)^{2}} as a single fraction.

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

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

$$\frac{2\left(-z^{3}\right)^{2}}{z^{4}}z^{2}$$

Calculate -z^{3} to the power of 2 and get \left(z^{3}\right)^{2}.

$$\frac{2\left(z^{3}\right)^{2}}{z^{4}}z^{2}$$

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

$$\frac{2z^{6}}{z^{4}}z^{2}$$

Cancel out z^{4} in both numerator and denominator.

$$2z^{2}z^{2}$$

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

$$2z^{4}$$