Solve frac{(-3x^{2}y)(4x^{-3}y^3)^2}{9x^-4y^3}

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

Evaluate

$$-\frac{16y^{4}}{3}$$

Solution Steps

Cancel out 3y in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{-\left(4x^{-3}y^{3}\right)^{2}x^{6}}{3y^{2}}$$

Expand \left(4x^{-3}y^{3}\right)^{2}.

$$\frac{-4^{2}\left(x^{-3}\right)^{2}\left(y^{3}\right)^{2}x^{6}}{3y^{2}}$$

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

$$\frac{-4^{2}x^{-6}\left(y^{3}\right)^{2}x^{6}}{3y^{2}}$$

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

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

Calculate 4 to the power of 2 and get 16.

$$\frac{-16x^{-6}y^{6}x^{6}}{3y^{2}}$$

Multiply x^{-6} and x^{6} to get 1.

$$\frac{-16y^{6}}{3y^{2}}$$

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

$$\frac{-16y^{4}}{3}$$

Expand

$$-\frac{16y^{4}}{3}$$

Solution Steps

Cancel out 3y in both numerator and denominator.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{-\left(4x^{-3}y^{3}\right)^{2}x^{6}}{3y^{2}}$$

Expand \left(4x^{-3}y^{3}\right)^{2}.

$$\frac{-4^{2}\left(x^{-3}\right)^{2}\left(y^{3}\right)^{2}x^{6}}{3y^{2}}$$

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

$$\frac{-4^{2}x^{-6}\left(y^{3}\right)^{2}x^{6}}{3y^{2}}$$

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

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

Calculate 4 to the power of 2 and get 16.

$$\frac{-16x^{-6}y^{6}x^{6}}{3y^{2}}$$

Multiply x^{-6} and x^{6} to get 1.

$$\frac{-16y^{6}}{3y^{2}}$$

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

$$\frac{-16y^{4}}{3}$$