Solve frac{2xy^{3}*(2y^{2}z^-1)^4}{y^3z^-3}

$$\frac { 2 x y ^ { 3 } \cdot ( 2 y ^ { 2 } z ^ { - 1 } ) ^ { 4 } } { y ^ { 3 } z ^ { - 3 } }$$

Evaluate

$$\frac{32xy^{8}}{z}$$

Solution Steps

Cancel out y^{3} in both numerator and denominator.

$$\frac{2x\times \left(2\times \frac{1}{z}y^{2}\right)^{4}}{z^{-3}}$$

Express 2\times \frac{1}{z} as a single fraction.

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

Express \frac{2}{z}y^{2} as a single fraction.

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

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

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

Express 2\times \frac{\left(2y^{2}\right)^{4}}{z^{4}} as a single fraction.

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

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

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

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

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

Calculate 2 to the power of 4 and get 16.

$$\frac{\frac{2\times 16y^{8}}{z^{4}}x}{z^{-3}}$$

Multiply 2 and 16 to get 32.

$$\frac{\frac{32y^{8}}{z^{4}}x}{z^{-3}}$$

Express \frac{32y^{8}}{z^{4}}x as a single fraction.

$$\frac{\frac{32y^{8}x}{z^{4}}}{z^{-3}}$$

Express \frac{\frac{32y^{8}x}{z^{4}}}{z^{-3}} as a single fraction.

$$\frac{32y^{8}x}{z^{4}z^{-3}}$$

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

$$\frac{32y^{8}x}{z^{1}}$$

Calculate z to the power of 1 and get z.

$$\frac{32y^{8}x}{z}$$

Expand

$$\frac{32xy^{8}}{z}$$

Solution Steps

Cancel out y^{3} in both numerator and denominator.

$$\frac{2x\times \left(2\times \frac{1}{z}y^{2}\right)^{4}}{z^{-3}}$$

Express 2\times \frac{1}{z} as a single fraction.

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

Express \frac{2}{z}y^{2} as a single fraction.

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

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

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

Express 2\times \frac{\left(2y^{2}\right)^{4}}{z^{4}} as a single fraction.

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

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

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

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

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

Calculate 2 to the power of 4 and get 16.

$$\frac{\frac{2\times 16y^{8}}{z^{4}}x}{z^{-3}}$$

Multiply 2 and 16 to get 32.

$$\frac{\frac{32y^{8}}{z^{4}}x}{z^{-3}}$$

Express \frac{32y^{8}}{z^{4}}x as a single fraction.

$$\frac{\frac{32y^{8}x}{z^{4}}}{z^{-3}}$$

Express \frac{\frac{32y^{8}x}{z^{4}}}{z^{-3}} as a single fraction.

$$\frac{32y^{8}x}{z^{4}z^{-3}}$$

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

$$\frac{32y^{8}x}{z^{1}}$$

Calculate z to the power of 1 and get z.

$$\frac{32y^{8}x}{z}$$