Raising a Monomial to a Power Help

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 .

Examples

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

Answers

5. 343x ¹⁵ y ⁶

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