Solve 5x^-2y^3*10x^-3y^-4

$$5 x ^ { - 2 } y ^ { 3 } \cdot 10 x ^ { - 3 } y ^ { - 4 }$$

Evaluate

$$\frac{50}{yx^{5}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$5^{1}x^{-2}y^{3}\times 10^{1}x^{-3}y^{-4}$$

Use the Commutative Property of Multiplication.

$$5^{1}\times 10^{1}x^{-2}x^{-3}y^{3}y^{-4}$$

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

$$5^{1}\times 10^{1}x^{-2-3}y^{3-4}$$

Add the exponents -2 and -3.

$$5^{1}\times 10^{1}x^{-5}y^{3-4}$$

Add the exponents 3 and -4.

$$5^{1}\times 10^{1}\times \frac{1}{x^{5}}\times \frac{1}{y}$$

Multiply 5 times 10.

$$50\times \frac{1}{x^{5}}\times \frac{1}{y}$$

Differentiate w.r.t. x

$$-\frac{250}{yx^{6}}$$