Solve (3u^7v^3)(4u^4v^-5)

$$( 3 u ^ { 7 } v ^ { 3 } ) ( 4 u ^ { 4 } v ^ { - 5 } )$$

Evaluate

$$\frac{12u^{11}}{v^{2}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$3^{1}u^{7}v^{3}\times 4^{1}u^{4}v^{-5}$$

Use the Commutative Property of Multiplication.

$$3^{1}\times 4^{1}u^{7}u^{4}v^{3}v^{-5}$$

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

$$3^{1}\times 4^{1}u^{7+4}v^{3-5}$$

Add the exponents 7 and 4.

$$3^{1}\times 4^{1}u^{11}v^{3-5}$$

Add the exponents 3 and -5.

$$3^{1}\times 4^{1}u^{11}v^{-2}$$

Multiply 3 times 4.

$$12u^{11}\times \frac{1}{v^{2}}$$

Differentiate w.r.t. u

$$\frac{132u^{10}}{v^{2}}$$