Solve frac{(2z^{2})^3-2z^2*3z^4}{(3z)^2}

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

Evaluate

$$\frac{2z^{4}}{9}$$

Solution Steps

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

$$\frac{\left(2z^{2}\right)^{3}-2z^{6}\times 3}{\left(3z\right)^{2}}$$

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

$$\frac{2^{3}\left(z^{2}\right)^{3}-2z^{6}\times 3}{\left(3z\right)^{2}}$$

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

$$\frac{2^{3}z^{6}-2z^{6}\times 3}{\left(3z\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8z^{6}-2z^{6}\times 3}{\left(3z\right)^{2}}$$

Multiply 2 and 3 to get 6.

$$\frac{8z^{6}-6z^{6}}{\left(3z\right)^{2}}$$

Combine 8z^{6} and -6z^{6} to get 2z^{6}.

$$\frac{2z^{6}}{\left(3z\right)^{2}}$$

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

$$\frac{2z^{6}}{3^{2}z^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2z^{6}}{9z^{2}}$$

Cancel out z^{2} in both numerator and denominator.

$$\frac{2z^{4}}{9}$$

Expand

$$\frac{2z^{4}}{9}$$

Solution Steps

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

$$\frac{\left(2z^{2}\right)^{3}-2z^{6}\times 3}{\left(3z\right)^{2}}$$

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

$$\frac{2^{3}\left(z^{2}\right)^{3}-2z^{6}\times 3}{\left(3z\right)^{2}}$$

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

$$\frac{2^{3}z^{6}-2z^{6}\times 3}{\left(3z\right)^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8z^{6}-2z^{6}\times 3}{\left(3z\right)^{2}}$$

Multiply 2 and 3 to get 6.

$$\frac{8z^{6}-6z^{6}}{\left(3z\right)^{2}}$$

Combine 8z^{6} and -6z^{6} to get 2z^{6}.

$$\frac{2z^{6}}{\left(3z\right)^{2}}$$

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

$$\frac{2z^{6}}{3^{2}z^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2z^{6}}{9z^{2}}$$

Cancel out z^{2} in both numerator and denominator.

$$\frac{2z^{4}}{9}$$