Solve left(3x^2y^2right)^2*-15xy^2/-9{x^4{y}^2}

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

Evaluate

$$15xy^{4}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$3^{2}x^{4}y^{4}\times \frac{-15xy^{2}}{-9x^{4}y^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{4}y^{4}\times \frac{-15xy^{2}}{-9x^{4}y^{2}}$$

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

$$9x^{4}y^{4}\times \frac{-5}{-3x^{3}}$$

Express 9\times \frac{-5}{-3x^{3}} as a single fraction.

$$\frac{9\left(-5\right)}{-3x^{3}}x^{4}y^{4}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-5\times 3}{-x^{3}}x^{4}y^{4}$$

Multiply -5 and 3 to get -15.

$$\frac{-15}{-x^{3}}x^{4}y^{4}$$

Express \frac{-15}{-x^{3}}x^{4} as a single fraction.

$$\frac{-15x^{4}}{-x^{3}}y^{4}$$

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

$$\frac{-15x}{-1}y^{4}$$

Express \frac{-15x}{-1}y^{4} as a single fraction.

$$\frac{-15xy^{4}}{-1}$$

Expand

$$15xy^{4}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$3^{2}x^{4}y^{4}\times \frac{-15xy^{2}}{-9x^{4}y^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$9x^{4}y^{4}\times \frac{-15xy^{2}}{-9x^{4}y^{2}}$$

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

$$9x^{4}y^{4}\times \frac{-5}{-3x^{3}}$$

Express 9\times \frac{-5}{-3x^{3}} as a single fraction.

$$\frac{9\left(-5\right)}{-3x^{3}}x^{4}y^{4}$$

Cancel out 3 in both numerator and denominator.

$$\frac{-5\times 3}{-x^{3}}x^{4}y^{4}$$

Multiply -5 and 3 to get -15.

$$\frac{-15}{-x^{3}}x^{4}y^{4}$$

Express \frac{-15}{-x^{3}}x^{4} as a single fraction.

$$\frac{-15x^{4}}{-x^{3}}y^{4}$$

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

$$\frac{-15x}{-1}y^{4}$$

Express \frac{-15x}{-1}y^{4} as a single fraction.

$$\frac{-15xy^{4}}{-1}$$