Solve (2r^3s^2)(4r^2s^5)

$$( 2 r ^ { 3 } s ^ { 2 } ) ( 4 r ^ { 2 } s ^ { 5 } )$$

Evaluate

$$8r^{5}s^{7}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$2^{1}r^{3}s^{2}\times 4^{1}r^{2}s^{5}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times 4^{1}r^{3}r^{2}s^{2}s^{5}$$

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

$$2^{1}\times 4^{1}r^{3+2}s^{2+5}$$

Add the exponents 3 and 2.

$$2^{1}\times 4^{1}r^{5}s^{2+5}$$

Add the exponents 2 and 5.

$$2^{1}\times 4^{1}r^{5}s^{7}$$

Multiply 2 times 4.

$$8r^{5}s^{7}$$

Differentiate w.r.t. r

$$40r^{4}s^{7}$$