Solve (-3x^5y^-8)(5x^-1y)

$$( - 3 x ^ { 5 } y ^ { - 8 } ) ( 5 x ^ { - 1 } y )$$

Evaluate

$$-\frac{15x^{4}}{y^{7}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-3\right)^{1}x^{5}y^{-8}\times 5^{1}\times \frac{1}{x}y^{1}$$

Use the Commutative Property of Multiplication.

$$\left(-3\right)^{1}\times 5^{1}x^{5}\times \frac{1}{x}y^{-8}y^{1}$$

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

$$\left(-3\right)^{1}\times 5^{1}x^{5-1}y^{-8+1}$$

Add the exponents 5 and -1.

$$\left(-3\right)^{1}\times 5^{1}x^{4}y^{-8+1}$$

Add the exponents -8 and 1.

$$\left(-3\right)^{1}\times 5^{1}x^{4}y^{-7}$$

Multiply -3 times 5.

$$-15x^{4}\times \frac{1}{y^{7}}$$

Differentiate w.r.t. x

$$-\frac{60x^{3}}{y^{7}}$$