Solve 2a^3left(b^3right)^24a^3{b}^4

$$2 { a }^{ 3 } { \left( { b }^{ 3 } \right) }^{ 2 } 4 { a }^{ 3 } { b }^{ 4 }$$

Evaluate

$$8a^{6}b^{10}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$2a^{3}b^{6}\times 4a^{3}b^{4}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$2a^{6}b^{6}\times 4b^{4}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$2a^{6}b^{10}\times 4$$

Multiply 2 and 4 to get 8.

$$8a^{6}b^{10}$$

Differentiate w.r.t. a

$$48a^{5}b^{10}$$