Study Guide: Multiplying Monomials

These web-based activities were developed, during summer sessions from 1997 through 1999, by students at Mainland High School, located in Daytona Beach, FL. As part of Mainland's CCTT grant, the students were given permission by the book's publisher to convert the ancillary materials of the County's adopted Algebra 1 textbook (Glencoe Algebra 1 — ISBN: 9780028253282) into html format.

Study Guide
Multiplying Monomials

When you multiply monomials, you use the following rules for all numbers a and b and any integers m, n, and p.

	Rule	Example
Product of Powers	For any number a, and all integers m and n, a^m · aⁿ = a^{m + n}	a² · a⁶ = a^{2 + 6} = a⁸
Power of a Power	For any number a, and all integers m and n, (a^m)ⁿ = a^mn	(a²)⁶ = a^{2 · 6} = a¹²
Power of a Product	For all numbers a and b, and any integer m, (ab)^m = a^mb^m	(pq)⁴ = p⁴q⁴
Power of a Monomial	For all numbers a and b, and all integers m, n and p, (a^mbⁿ)^p = a^mpb^np	(s⁴t)³ = (s⁴ t¹)³ = s^{4 · 3} t^{1 · 3} = s¹² t³

n⁷

b⁵

−7x⁶

16a³

r² s⁶

4x³ y⁴

4a³ b⁴

−20n⁵ x³

n¹⁵

a²⁴

−3a³ b¹²

−27a³ b¹²

64x⁶ b³

16x² b³

4m¹⁰ n¹²

−2m⁵ n¹²

54x³

−96x⁵

12n¹² y¹⁰

−243a¹⁵ n⁸