Solve (-5x^5y^-4)(3x^-2y^2)

$$( - 5 x ^ { 5 } y ^ { - 4 } ) ( 3 x ^ { - 2 } y ^ { 2 } )$$

Evaluate

$$-\frac{15x^{3}}{y^{2}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-5\right)^{1}x^{5}y^{-4}\times 3^{1}x^{-2}y^{2}$$

Use the Commutative Property of Multiplication.

$$\left(-5\right)^{1}\times 3^{1}x^{5}x^{-2}y^{-4}y^{2}$$

To multiply powers of the same base, add their exponents.

$$\left(-5\right)^{1}\times 3^{1}x^{5-2}y^{-4+2}$$

Add the exponents 5 and -2.

$$\left(-5\right)^{1}\times 3^{1}x^{3}y^{-4+2}$$

Add the exponents -4 and 2.

$$\left(-5\right)^{1}\times 3^{1}x^{3}y^{-2}$$

Multiply -5 times 3.

$$-15x^{3}\times \frac{1}{y^{2}}$$

Differentiate w.r.t. x

$$-45\times \left(\frac{x}{y}\right)^{2}$$