How to Multiply Monomials

Example 1 Let's multiply the following 2 monomials:

(5x )(3x²y)

Step 1) Group variables by exponent and group the coefficients (apply commutative property of multiplication)

(5 • 3)(x • x2)(y)

Step 2) Multiply each like term (remember your exponents laws)

(5 • 3)(x • x2)(y)=(15)( x(2+1))(y) 15x3y

Video Tutorial on How To Multiply Monomials

Problem 1) Multiply the following 2 monomials:

(2x )(4x³k)

Step 1

Step 1) Group variables by exponent and group the coefficients (apply commutative property of multiplication)

(2 • 4)(x • x3)(k)

Step 2

Step 2) Multiply each like term (remember your exponents laws)

(2 • 4)(x • x3)(k) = (8)( x(1 + 3))(k) 8x4k

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Problem 2) Multiply the monomials below

(5x²k⁴)(7x⁵k)

Step 1

Step 1) Group variables by exponent and group the coefficients (apply commutative property of multiplication)

(5 • 7)(x2 • x5)(k4 • k)

Step 2

Step 2) Multiply each like term (remember the exponents rules)

(5 • 7)(x2 • x5)(k4 • k) (35)( x(2 + 4))(k(4 + 1)) 35 x6 k5

Problem 3) Multiply the monomials below

(6x⁴k⁸)(2x³k)(5x²k³z¹²)

Step 1

Step 1) Group variables by exponent and group the coefficients (apply commutative property of multiplication)

(6 • 2 • 5)(x4 • x3 • x2)(k8 • k)(z)

Step 2

Step 2) Multiply each like term (remember the exponents rules)

(6 • 2 • 5)(x4 • x3 • x2)(k8 • k)(z) (60)( x(4 + 3 + 2))(k(8 + 1))(z) 60 x9k9 z

Problem ) Multiply the following 2 monomials

( 7a⁴t⁷ )( 3t³a⁶k² ) ( 9t²²k⁴f⁵ )

Step 1

Step 1) Group variables by exponent and group the coefficients (apply commutative property of multiplication)

( 7 • 3 • 9 )( a4 • a5 ) ( t7 • t3 • t5 )( k2 • k4 )(f)

Step 2

Step 2) Multiply each like term (remember the exponents rules)

( 7 • 3 • 9 )( a4 • a5 ) ( t7 • t3 • t5 )( k2 • k4 )(f) (189)( a(4 + 5))(t(7 + 3 + 5 ))( k(2 + 4))( f) 189 a9 t15 k6f