Solve (2x^{2}y)^3x(-15xy^3)div(-9x^4y^2)

$$( 2 x ^ { 2 } y ) ^ { 3 } x ( - 15 x y ^ { 3 } ) \div ( - 9 x ^ { 4 } y ^ { 2 } )$$

Evaluate

$$\frac{40\left(xy\right)^{4}}{3}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{\left(2x^{2}y\right)^{3}x^{2}\left(-15\right)y^{3}}{-9x^{4}y^{2}}$$

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

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

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

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

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

$$\frac{-5y\times 2^{3}y^{3}x^{6}}{-3x^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-5y\times 8y^{3}x^{6}}{-3x^{2}}$$

Multiply -5 and 8 to get -40.

$$\frac{-40yy^{3}x^{6}}{-3x^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{-40y^{4}x^{6}}{-3x^{2}}$$

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

$$\frac{-40x^{4}y^{4}}{-3}$$

Expand

$$\frac{40\left(xy\right)^{4}}{3}$$

Solution Steps

Multiply x and x to get x^{2}.

$$\frac{\left(2x^{2}y\right)^{3}x^{2}\left(-15\right)y^{3}}{-9x^{4}y^{2}}$$

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

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

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

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

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

$$\frac{-5y\times 2^{3}y^{3}x^{6}}{-3x^{2}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-5y\times 8y^{3}x^{6}}{-3x^{2}}$$

Multiply -5 and 8 to get -40.

$$\frac{-40yy^{3}x^{6}}{-3x^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{-40y^{4}x^{6}}{-3x^{2}}$$

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

$$\frac{-40x^{4}y^{4}}{-3}$$