Solve w^{10}x^5divw^3x/2y^4*(4y/x)^3

$$w ^ { 10 } x ^ { 5 } \div \frac { w ^ { 3 } x } { 2 y ^ { 4 } } \times ( \frac { 4 y } { x } ) ^ { 3 }$$

Evaluate

$$128x\left(wy\right)^{7}$$

Solution Steps

Divide w^{10}x^{5} by \frac{w^{3}x}{2y^{4}} by multiplying w^{10}x^{5} by the reciprocal of \frac{w^{3}x}{2y^{4}}.

$$\frac{w^{10}x^{5}\times 2y^{4}}{w^{3}x}\times \left(\frac{4y}{x}\right)^{3}$$

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

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

To raise \frac{4y}{x} to a power, raise both numerator and denominator to the power and then divide.

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

Express 2\times \frac{\left(4y\right)^{3}}{x^{3}} as a single fraction.

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

Expand \left(4y\right)^{3}.

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

Calculate 4 to the power of 3 and get 64.

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

Multiply 2 and 64 to get 128.

$$\frac{128y^{3}}{x^{3}}x^{4}y^{4}w^{7}$$

Express \frac{128y^{3}}{x^{3}}x^{4} as a single fraction.

$$\frac{128y^{3}x^{4}}{x^{3}}y^{4}w^{7}$$

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

$$128xy^{3}y^{4}w^{7}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$128xy^{7}w^{7}$$

Expand

$$128x\left(wy\right)^{7}$$

Solution Steps

Divide w^{10}x^{5} by \frac{w^{3}x}{2y^{4}} by multiplying w^{10}x^{5} by the reciprocal of \frac{w^{3}x}{2y^{4}}.

$$\frac{w^{10}x^{5}\times 2y^{4}}{w^{3}x}\times \left(\frac{4y}{x}\right)^{3}$$

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

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

To raise \frac{4y}{x} to a power, raise both numerator and denominator to the power and then divide.

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

Express 2\times \frac{\left(4y\right)^{3}}{x^{3}} as a single fraction.

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

Expand \left(4y\right)^{3}.

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

Calculate 4 to the power of 3 and get 64.

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

Multiply 2 and 64 to get 128.

$$\frac{128y^{3}}{x^{3}}x^{4}y^{4}w^{7}$$

Express \frac{128y^{3}}{x^{3}}x^{4} as a single fraction.

$$\frac{128y^{3}x^{4}}{x^{3}}y^{4}w^{7}$$

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

$$128xy^{3}y^{4}w^{7}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$128xy^{7}w^{7}$$