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Multiplying Monomials and Raising Monomials to Powers

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1 Multiplying Monomials and Raising Monomials to Powers

2 Vocabulary Monomials - a number, a variable, or a product of a number and one or more variables 4x, 20x2yw3, -3, a2b3, and 3yz are all monomials. Constant – a monomial that is a number without a variable. Base – In an expression of the form xn, the base is x. Exponent – In an expression of the form xn, the exponent is n.

3 Writing - Using Exponents
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.

4 Writing Expressions without Exponents
Write out each expression without exponents (as multiplication): or

5 Product of Powers Simplify the following expression: (5a2)(a5)
Step 1: Write out the expressions in expanded form. Step 2: Rewrite using exponents.

6 Product of Powers Rule am • an = am+n.
For any number a, and all integers m and n, am • an = am+n.

7 Multiplying Monomials
If the monomials have coefficients, multiply those, but still add the powers.

8 Multiplying Monomials
These monomials have a mixture of different variables. Only add powers of like variables.

9 The monomial is the term inside the parentheses.
Power of Powers Simplify the following: ( x3 ) 4 The monomial is the term inside the parentheses. Write out the expression in expanded form. Simplify, writing as a power. Note: 3 x 4 = 12.

10 Power of Powers Rule For any number, a, and all integers m and n,

11 Monomials to Powers If the monomial inside the parentheses has a coefficient, raise the coefficient to the power, but still multiply the variable powers.

12 Monomials to Powers (Power of a Product)
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

13 Monomials to Powers (Power of a Product)
Simplify each expression:

14 Special Case 1 X0=1 (ab)0 = 1 50=1 00=1 or undefined
Any base raised to the power of zero (except zero) equals one. X0= (ab)0 = =1 00=1 or undefined Simplify each expression:

15 Special Case 2 Any base raised to a negative power becomes the denominator of a fraction Simplify each expression:


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