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# Raising a Monomial to a Power Help

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## Raising a Monomial to a Power

When a variable is raised to a power, the exponent of the variable is multiplied by the power. For example,

(x 2 ) 3 = x 2 · x 2 · x 2 · = x 2+2+2 = x 6

or

(x 2 ) 3 = x 2 · 3 = x 6

In general (x m ) n = x m·n . To raise a monomial to a power, raise the numerical coefficient to the power and multiply the exponents of the variables by the power .

#### Example 1

Find (5x 3 y 4 ) 2

#### Example 2

Find (-6a 4 b 5 ) 3 .

#### Example 3

Find (-xy 3 ) 4 .

### Raising a Monomial to a Power Practice Problems

#### Practice

Find each of the following:

1. (x 4 ) 5

2. (3a) 2

3. (6m 2 n 4 ) 3

4. (-5a 3 b 2 ) 2

5. (7x 5 y 2 ) 3

1. x 20

2. 9a 2

3. 216 m 6 n 12

4. 25a 6 b 4

5. 343x 15 y 6

Practice problems for these concepts can be found at: Operations with Monomials and Polynomials Practice Test.

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