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

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

Evaluate

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

Solution Steps

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

$$\frac{2x^{2}y^{2}z^{6}\times 2}{\left(z^{4}y^{2}\right)^{3}}$$

Multiply 2 and 2 to get 4.

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

Expand \left(z^{4}y^{2}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{4x^{2}y^{2}z^{6}}{z^{12}\left(y^{2}\right)^{3}}$$

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

$$\frac{4x^{2}y^{2}z^{6}}{z^{12}y^{6}}$$

Cancel out y^{2}z^{6} in both numerator and denominator.

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

Expand

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

Solution Steps

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

$$\frac{2x^{2}y^{2}z^{6}\times 2}{\left(z^{4}y^{2}\right)^{3}}$$

Multiply 2 and 2 to get 4.

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

Expand \left(z^{4}y^{2}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{4x^{2}y^{2}z^{6}}{z^{12}\left(y^{2}\right)^{3}}$$

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

$$\frac{4x^{2}y^{2}z^{6}}{z^{12}y^{6}}$$

Cancel out y^{2}z^{6} in both numerator and denominator.

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