Solve frac{zx^{3}*2yx^{2}z^3}{y^3*(-2xz^2)^4}

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

Evaluate

$$\frac{x}{8y^{2}z^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

Cancel out y in both numerator and denominator.

$$\frac{2z^{4}x^{5}}{y^{2}\left(-2xz^{2}\right)^{4}}$$

Expand \left(-2xz^{2}\right)^{4}.

$$\frac{2z^{4}x^{5}}{y^{2}\left(-2\right)^{4}x^{4}\left(z^{2}\right)^{4}}$$

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

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

Calculate -2 to the power of 4 and get 16.

$$\frac{2z^{4}x^{5}}{y^{2}\times 16x^{4}z^{8}}$$

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

$$\frac{x}{8y^{2}z^{4}}$$

Expand

$$\frac{x}{8y^{2}z^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

Cancel out y in both numerator and denominator.

$$\frac{2z^{4}x^{5}}{y^{2}\left(-2xz^{2}\right)^{4}}$$

Expand \left(-2xz^{2}\right)^{4}.

$$\frac{2z^{4}x^{5}}{y^{2}\left(-2\right)^{4}x^{4}\left(z^{2}\right)^{4}}$$

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

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

Calculate -2 to the power of 4 and get 16.

$$\frac{2z^{4}x^{5}}{y^{2}\times 16x^{4}z^{8}}$$

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

$$\frac{x}{8y^{2}z^{4}}$$