Solve -3x^-2y^5*-9yx^-4=

$$- 3 x ^ { - 2 } y ^ { 5 } \cdot - 9 y x ^ { - 4 } =$$

Evaluate

$$27\times \left(\frac{y}{x}\right)^{6}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-3\right)^{1}x^{-2}y^{5}\left(-9\right)^{1}x^{-4}y^{1}$$

Use the Commutative Property of Multiplication.

$$\left(-3\right)^{1}\left(-9\right)^{1}x^{-2}x^{-4}y^{5}y^{1}$$

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

$$\left(-3\right)^{1}\left(-9\right)^{1}x^{-2-4}y^{5+1}$$

Add the exponents -2 and -4.

$$\left(-3\right)^{1}\left(-9\right)^{1}x^{-6}y^{5+1}$$

Add the exponents 5 and 1.

$$\left(-3\right)^{1}\left(-9\right)^{1}\times \frac{1}{x^{6}}y^{6}$$

Multiply -3 times -9.

$$27\times \frac{1}{x^{6}}y^{6}$$

Differentiate w.r.t. x

$$-\frac{162y^{6}}{x^{7}}$$