Solve 2a^-5b^6*5a^2b^2

$$2 a ^ { - 5 } b ^ { 6 } \cdot 5 a ^ { 2 } b ^ { 2 }$$

Evaluate

$$\frac{10b^{8}}{a^{3}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$2^{1}a^{-5}b^{6}\times 5^{1}a^{2}b^{2}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times 5^{1}a^{-5}a^{2}b^{6}b^{2}$$

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

$$2^{1}\times 5^{1}a^{-5+2}b^{6+2}$$

Add the exponents -5 and 2.

$$2^{1}\times 5^{1}a^{-3}b^{6+2}$$

Add the exponents 6 and 2.

$$2^{1}\times 5^{1}\times \frac{1}{a^{3}}b^{8}$$

Multiply 2 times 5.

$$10\times \frac{1}{a^{3}}b^{8}$$

Differentiate w.r.t. b

$$\frac{80b^{7}}{a^{3}}$$