Solve (3x^-6q^3)(-5x^2q^-6)

$$( 3 x ^ { - 6 } q ^ { 3 } ) ( - 5 x ^ { 2 } q ^ { - 6 } )$$

Evaluate

$$-\frac{15}{q^{3}x^{4}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$3^{1}x^{-6}q^{3}\left(-5\right)^{1}x^{2}q^{-6}$$

Use the Commutative Property of Multiplication.

$$3^{1}\left(-5\right)^{1}x^{-6}x^{2}q^{3}q^{-6}$$

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

$$3^{1}\left(-5\right)^{1}x^{-6+2}q^{3-6}$$

Add the exponents -6 and 2.

$$3^{1}\left(-5\right)^{1}x^{-4}q^{3-6}$$

Add the exponents 3 and -6.

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

Multiply 3 times -5.

$$-15\times \frac{1}{x^{4}}\times \frac{1}{q^{3}}$$

Differentiate w.r.t. x

$$\frac{60}{q^{3}x^{5}}$$