Multiplication
4-4Powers of Monomials
Overview
(a^m)^n = a^(mn). Also (ab)^n = a^n · b^n.
Key ideas
- Power of a power: multiply exponents.
- Power of a product: distribute the exponent.
- Apply to coefficient and to every variable.
Worked examples
Example 1
Problem. (x^3)^4
Solution. x^12
Example 2
Problem. (2y^2)^3
Solution. 8y^6
Practice
Try each one. Click Show answer when ready.
- 1.
(a^5)^2
- 2.
(3x)^4
- 3.
(−2m^2n)^3
Challenge problems
A little tougher — great for test prep. Click Show answer when ready.
- 1.
Simplify (−2x³y²)⁴.
- 2.
Simplify (3a²b³)²(−2ab)³.