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# Multiplication of Monomials Help

based on 2 ratings
By McGraw-Hill Professional
Updated on Sep 26, 2011

## Multiplication of Monomials

### Multiplying Variables with Exponents

When two variables with the same base are multiplied, the exponents of the variables are added to get the product. For example,

x 3 · x 4 = x · x · x · x · x · x · x = x 3+4 = x 7

In general,

x m · x n = x m+n

#### Example 1

Multiply y 5 · y 6.

#### Solution 1

y 5 · y 6 = y 5+6 = y 11

### Multiplying Two Monomials

To multiply two monomials, multiply the numerical coefficients (numbers) and add the exponents of the same variables (letters).

#### Example 2

Multiply 5x 3 y 2 · 3x 2 y 4

#### Example 3

Multiple - 3m 5 n 4 · 6m 2 · n 6 .

#### Solution 3

Math Note: Recall that x = x 1 .

#### Example 4

Multiply - xy · 2x 2 y 3

### Multiplication of Monomials Practice Problems

#### Practice

Multiply:

1. 2xy · 5xy

2. -8a 2 · 2a 3 b 2

3. 4x 3 y · 3x 2 y 2 · 5xy

4.-9ab 4 · 6ab 2 · 3ab

5. 7xy · 3x 2 z ·(-2yxz 2 )

1. 10x 2 y 2

2. -16a 5 b 2

3. 60x 6 y 4

4. -162a 3 b 7

5. -42x 3 y 2 z 3

Practice problems for these concepts can be found at: Operations With Monomials And Polynomials Practice Test.

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