Solve frac{x2y^{2}*2x^{4}y^{2}z^3}{(2yx^4z^3)^2}

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

Evaluate

$$\frac{x_{2}y^{2}}{2z^{3}x^{4}}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{x_{2}y^{4}\times 2x^{4}z^{3}}{2^{2}y^{2}x^{8}\left(z^{3}\right)^{2}}$$

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

$$\frac{x_{2}y^{4}\times 2x^{4}z^{3}}{2^{2}y^{2}x^{8}z^{6}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x_{2}y^{4}\times 2x^{4}z^{3}}{4y^{2}x^{8}z^{6}}$$

Cancel out 2y^{2}z^{3}x^{4} in both numerator and denominator.

$$\frac{x_{2}y^{2}}{2z^{3}x^{4}}$$

Expand

$$\frac{x_{2}y^{2}}{2z^{3}x^{4}}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{x_{2}y^{4}\times 2x^{4}z^{3}}{2^{2}y^{2}x^{8}\left(z^{3}\right)^{2}}$$

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

$$\frac{x_{2}y^{4}\times 2x^{4}z^{3}}{2^{2}y^{2}x^{8}z^{6}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x_{2}y^{4}\times 2x^{4}z^{3}}{4y^{2}x^{8}z^{6}}$$

Cancel out 2y^{2}z^{3}x^{4} in both numerator and denominator.

$$\frac{x_{2}y^{2}}{2z^{3}x^{4}}$$