Solve (4y^2z^3x^7)(2y/x)^4

$$( 4 y ^ { 2 } z ^ { 3 } x ^ { 7 } ) ( \frac { 2 y } { x } ) ^ { 4 }$$

Evaluate

$$64y^{6}\left(xz\right)^{3}$$

Solution Steps

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

$$4y^{2}z^{3}x^{7}\times \frac{\left(2y\right)^{4}}{x^{4}}$$

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

$$\frac{4\times \left(2y\right)^{4}}{x^{4}}y^{2}z^{3}x^{7}$$

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

$$\frac{4\times 2^{4}y^{4}}{x^{4}}y^{2}z^{3}x^{7}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{4\times 16y^{4}}{x^{4}}y^{2}z^{3}x^{7}$$

Multiply 4 and 16 to get 64.

$$\frac{64y^{4}}{x^{4}}y^{2}z^{3}x^{7}$$

Express \frac{64y^{4}}{x^{4}}y^{2} as a single fraction.

$$\frac{64y^{4}y^{2}}{x^{4}}z^{3}x^{7}$$

Express \frac{64y^{4}y^{2}}{x^{4}}z^{3} as a single fraction.

$$\frac{64y^{4}y^{2}z^{3}}{x^{4}}x^{7}$$

Express \frac{64y^{4}y^{2}z^{3}}{x^{4}}x^{7} as a single fraction.

$$\frac{64y^{4}y^{2}z^{3}x^{7}}{x^{4}}$$

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

$$64y^{2}x^{3}z^{3}y^{4}$$

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

$$64y^{6}x^{3}z^{3}$$

Expand

$$64y^{6}\left(xz\right)^{3}$$

Solution Steps

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

$$4y^{2}z^{3}x^{7}\times \frac{\left(2y\right)^{4}}{x^{4}}$$

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

$$\frac{4\times \left(2y\right)^{4}}{x^{4}}y^{2}z^{3}x^{7}$$

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

$$\frac{4\times 2^{4}y^{4}}{x^{4}}y^{2}z^{3}x^{7}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{4\times 16y^{4}}{x^{4}}y^{2}z^{3}x^{7}$$

Multiply 4 and 16 to get 64.

$$\frac{64y^{4}}{x^{4}}y^{2}z^{3}x^{7}$$

Express \frac{64y^{4}}{x^{4}}y^{2} as a single fraction.

$$\frac{64y^{4}y^{2}}{x^{4}}z^{3}x^{7}$$

Express \frac{64y^{4}y^{2}}{x^{4}}z^{3} as a single fraction.

$$\frac{64y^{4}y^{2}z^{3}}{x^{4}}x^{7}$$

Express \frac{64y^{4}y^{2}z^{3}}{x^{4}}x^{7} as a single fraction.

$$\frac{64y^{4}y^{2}z^{3}x^{7}}{x^{4}}$$

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

$$64y^{2}x^{3}z^{3}y^{4}$$

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

$$64y^{6}x^{3}z^{3}$$