Solve 6a^3b^4div2a^2b^3*3a{b}^2

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

Evaluate

$$9a^{6}b^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{6a^{3}b^{4}}{2}a^{3}b^{5}\times 3$$

Divide 6a^{3}b^{4} by 2 to get 3a^{3}b^{4}.

$$3a^{3}b^{4}a^{3}b^{5}\times 3$$

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

$$3a^{6}b^{4}b^{5}\times 3$$

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$3a^{6}b^{9}\times 3$$

Multiply 3 and 3 to get 9.

$$9a^{6}b^{9}$$

Differentiate w.r.t. a

$$54a^{5}b^{9}$$