Solve frac{(4x^{3})(2x^-1)^3}{(8y^2)(3y^-1)}

$$\frac { ( 4 x ^ { 3 } ) ( 2 x ^ { - 1 } ) ^ { 3 } } { ( 8 y ^ { 2 } ) ( 3 y ^ { - 1 } ) }$$

Evaluate

$$\frac{4}{3y}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -1 to get 1.

$$\frac{4x^{3}\times \left(2x^{-1}\right)^{3}}{8y^{1}\times 3}$$

Cancel out 4 in both numerator and denominator.

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

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

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

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

$$\frac{\frac{2^{3}}{x^{3}}x^{3}}{2\times 3y^{1}}$$

Cancel out x^{3} and x^{3}.

$$\frac{2^{3}}{2\times 3y^{1}}$$

Multiply 2 and 3 to get 6.

$$\frac{2^{3}}{6y^{1}}$$

Calculate y to the power of 1 and get y.

$$\frac{2^{3}}{6y}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8}{6y}$$

Expand

$$\frac{4}{3y}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -1 to get 1.

$$\frac{4x^{3}\times \left(2x^{-1}\right)^{3}}{8y^{1}\times 3}$$

Cancel out 4 in both numerator and denominator.

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

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

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

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

$$\frac{\frac{2^{3}}{x^{3}}x^{3}}{2\times 3y^{1}}$$

Cancel out x^{3} and x^{3}.

$$\frac{2^{3}}{2\times 3y^{1}}$$

Multiply 2 and 3 to get 6.

$$\frac{2^{3}}{6y^{1}}$$

Calculate y to the power of 1 and get y.

$$\frac{2^{3}}{6y}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8}{6y}$$