Solve (-9a^-6t^-6)(6a^-4t^-4)

$$( - 9 a ^ { - 6 } t ^ { - 6 } ) ( 6 a ^ { - 4 } t ^ { - 4 } )$$

Evaluate

$$-\frac{54}{\left(at\right)^{10}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-9\right)^{1}a^{-6}t^{-6}\times 6^{1}a^{-4}t^{-4}$$

Use the Commutative Property of Multiplication.

$$\left(-9\right)^{1}\times 6^{1}a^{-6}a^{-4}t^{-6}t^{-4}$$

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

$$\left(-9\right)^{1}\times 6^{1}a^{-6-4}t^{-6-4}$$

Add the exponents -6 and -4.

$$\left(-9\right)^{1}\times 6^{1}a^{-10}t^{-6-4}$$

Add the exponents -6 and -4.

$$\left(-9\right)^{1}\times 6^{1}\times \frac{1}{a^{10}}t^{-10}$$

Multiply -9 times 6.

$$-54\times \frac{1}{a^{10}}\times \frac{1}{t^{10}}$$

Differentiate w.r.t. a

$$\frac{540}{t^{10}a^{11}}$$