Solve -3a^2b^-3*3a^-5b^8=

$$- 3 a ^ { 2 } b ^ { - 3 } \cdot 3 a ^ { - 5 } b ^ { 8 } =$$

Evaluate

$$-\frac{9b^{5}}{a^{3}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-3\right)^{1}a^{2}b^{-3}\times 3^{1}a^{-5}b^{8}$$

Use the Commutative Property of Multiplication.

$$\left(-3\right)^{1}\times 3^{1}a^{2}a^{-5}b^{-3}b^{8}$$

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

$$\left(-3\right)^{1}\times 3^{1}a^{2-5}b^{-3+8}$$

Add the exponents 2 and -5.

$$\left(-3\right)^{1}\times 3^{1}a^{-3}b^{-3+8}$$

Add the exponents -3 and 8.

$$\left(-3\right)^{1}\times 3^{1}\times \frac{1}{a^{3}}b^{5}$$

Multiply -3 times 3.

$$-9\times \frac{1}{a^{3}}b^{5}$$

Differentiate w.r.t. b

$$-\frac{45b^{4}}{a^{3}}$$