Solve (2x^{2}y)^3*(-7xy^2)div(14x^4y^3)

$$( 2 x ^ { 2 } y ) ^ { 3 } \cdot ( - 7 x y ^ { 2 } ) \div ( 14 x ^ { 4 } y ^ { 3 } )$$

Evaluate

$$-4y^{2}x^{3}$$

Solution Steps

Cancel out 7xy^{2} in both numerator and denominator.

$$\frac{-\left(2yx^{2}\right)^{3}}{2yx^{3}}$$

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

$$\frac{-2^{3}y^{3}\left(x^{2}\right)^{3}}{2yx^{3}}$$

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

$$\frac{-2^{3}y^{3}x^{6}}{2yx^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-8y^{3}x^{6}}{2yx^{3}}$$

Cancel out 2yx^{3} in both numerator and denominator.

$$-4y^{2}x^{3}$$

Expand

$$-4y^{2}x^{3}$$

Solution Steps

Cancel out 7xy^{2} in both numerator and denominator.

$$\frac{-\left(2yx^{2}\right)^{3}}{2yx^{3}}$$

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

$$\frac{-2^{3}y^{3}\left(x^{2}\right)^{3}}{2yx^{3}}$$

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

$$\frac{-2^{3}y^{3}x^{6}}{2yx^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-8y^{3}x^{6}}{2yx^{3}}$$

Cancel out 2yx^{3} in both numerator and denominator.

$$-4y^{2}x^{3}$$