Monomials. Multiplying Monomials and Raising Monomials to Powers. Vocabulary. Monomials - a number, a variable, or a product of a number and one or more variables 4 x , 20 x 2 yw 3 , -3, a 2 b 3 , and 3 yz are all monomials. Constant – a monomial that is a number without a variable.
Multiplying Monomials and Raising Monomials to Powers
Rewrite the following expressions using exponents:
The variables, x and y, represent the bases. The number of times each base is multiplied by itself will be the value of the exponent.
Write out each expression without exponents (as multiplication):
Simplify the following expression: (5a2)(a5)
There are two monomials. Underline them.
What operation is between the two monomials?
For any number a, and all integers m and n,
am • an = am+n.
If the monomials have coefficients, multiply those, but still add the powers.
These monomials have a mixture of different variables. Only add powers of like variables.
Simplify the following: ( x3 )4
The monomial is the term inside the parentheses.
Note: 3 x 4 = 12.
If the monomial inside the parentheses has a coefficient, raise the coefficient to the power, but still multiply the variable powers.
If the monomial inside the parentheses has more than one variable, raise each variable to the outside power using the power of a power rule.
(ab)m = am•bm
Simplify each expression: