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

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

Evaluate

$$15xy^{3}$$

Solution Steps

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

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

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

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

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

$$\frac{-5y\times 3^{2}y^{2}x^{4}}{-3x^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{-5y\times 9y^{2}x^{4}}{-3x^{3}}$$

Multiply -5 and 9 to get -45.

$$\frac{-45yy^{2}x^{4}}{-3x^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{-45y^{3}x^{4}}{-3x^{3}}$$

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

$$\frac{-15xy^{3}}{-1}$$

Anything divided by -1 gives its opposite.

$$15xy^{3}$$

Expand

$$15xy^{3}$$

Solution Steps

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

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

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

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

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

$$\frac{-5y\times 3^{2}y^{2}x^{4}}{-3x^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{-5y\times 9y^{2}x^{4}}{-3x^{3}}$$

Multiply -5 and 9 to get -45.

$$\frac{-45yy^{2}x^{4}}{-3x^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\frac{-45y^{3}x^{4}}{-3x^{3}}$$

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

$$\frac{-15xy^{3}}{-1}$$

Anything divided by -1 gives its opposite.

$$15xy^{3}$$