Solve (frac{x^{4}z^{2}}{4y^{5}})(2x^3y^2/z^3)^2

$$( \frac { x ^ { 4 } z ^ { 2 } } { 4 y ^ { 5 } } ) ( \frac { 2 x ^ { 3 } y ^ { 2 } } { z ^ { 3 } } ) ^ { 2 }$$

Evaluate

$$\frac{x^{10}}{yz^{4}}$$

Solution Steps

To raise \frac{2x^{3}y^{2}}{z^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{x^{4}z^{2}}{4y^{5}} times \frac{\left(2x^{3}y^{2}\right)^{2}}{\left(z^{3}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

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

$$\frac{x^{4}z^{2}\times \left(2x^{3}y^{2}\right)^{2}}{4y^{5}z^{6}}$$

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

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

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

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

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

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

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

$$\frac{x^{4}\times 2^{2}y^{4}x^{6}}{4z^{4}y^{5}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{4}\times 4y^{4}x^{6}}{4z^{4}y^{5}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{x^{10}\times 4y^{4}}{4z^{4}y^{5}}$$

Cancel out 4y^{4} in both numerator and denominator.

$$\frac{x^{10}}{yz^{4}}$$

Expand

$$\frac{x^{10}}{yz^{4}}$$

Solution Steps

To raise \frac{2x^{3}y^{2}}{z^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Multiply \frac{x^{4}z^{2}}{4y^{5}} times \frac{\left(2x^{3}y^{2}\right)^{2}}{\left(z^{3}\right)^{2}} by multiplying numerator times numerator and denominator times denominator.

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

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

$$\frac{x^{4}z^{2}\times \left(2x^{3}y^{2}\right)^{2}}{4y^{5}z^{6}}$$

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

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

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

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

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

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

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

$$\frac{x^{4}\times 2^{2}y^{4}x^{6}}{4z^{4}y^{5}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{x^{4}\times 4y^{4}x^{6}}{4z^{4}y^{5}}$$

To multiply powers of the same base, add their exponents. Add 4 and 6 to get 10.

$$\frac{x^{10}\times 4y^{4}}{4z^{4}y^{5}}$$

Cancel out 4y^{4} in both numerator and denominator.

$$\frac{x^{10}}{yz^{4}}$$