Solve 3a^2ba^3b^5b^6

$$3 a ^ { 2 } b a ^ { 3 } b ^ { 5 } b ^ { 6 }$$

Evaluate

$$3a^{5}b^{12}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$3^{1}a^{2}b^{1}b^{5}a^{3}b^{6}$$

Use the Commutative Property of Multiplication.

$$3^{1}b^{5}a^{2}a^{3}b^{1}b^{6}$$

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

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

Add the exponents 2 and 3.

$$3^{1}b^{5}a^{5}b^{1+6}$$

Add the exponents 1 and 6.

$$3^{1}b^{5}a^{5}b^{7}$$

Raise b to the power 5.

$$3b^{5}a^{5}b^{7}$$

Differentiate w.r.t. a

$$15a^{4}b^{12}$$