Products & Quotients of Monomials

A monomial is a number, a variable or a product of a number and one or more variables.

Examples: 56, t, s, 24x² , and (xyz⁴ ) / 7

m/n is not a monomial, since it is a quotient of two variables.

Reminder: In the monomial x⁴ , the x is the base, and the 4 is the exponent.

I. To multiply two powers that have the same base, add the exponents.

(x⁵) (x⁷) = x⁵⁺⁷ = x¹²

II. To find the powers of a power, multiply all the exponents.

(m⁷ )² = m¹⁴

III. To find the power of a product, find the power of each factor and multiply.

( - 3ab)³ = ( - 3)³ a³ b³  = - 27a³ b³

IV.  To divide two powers that have the same base, subtract the exponents.

x¹² / x³ = x^{(12 - 3)} = x⁹ 

V. To find the power of a quotient, find the power of the numerator and the denominator.

( 3b² / 4)³ = (3b² )³ / (4)³ = 27b⁶ / 64

VI. Any nonzero number raised to the zero power is 1.

( - 7a³ b³ / 8 ab)⁰ = 1