Matemáticas

Sec 7-1
Multiplying Monomials
Monomials A monomial is a number, a variable, or the product of a number and one or more variables withnonnegative integer exponents. An expression of the form xn is called a power and represents the product you obtain when x is used as a factor ntimes. To multiply two powers that have the same base, add the exponents.
Product of Powers | For any number a and all integers m and n, am· an = am + n. |

Example 1 Simplify (3x6)(5x2). | Example 2 Simplify (-4a3b)(3a2b5). |
Simplify each expression.
1. y(y5)

2.(-7x2)(x4)

3. (-x3)(-x4)

4. (2a3b)(6b3)

5. (-3j2k4)(2jk6)

6. (10x3yz2)(-2xy5z)

Simplify Expressions Anexpression of the form (xm)n is called a power of a power and represents the product you obtain when xm is used as a factor n times. To find thepower of a power, multiply exponents.
Power of a Power | For any number a and all integers m and n, (am)n = amn. |
Power of a Product | Forany number a and all integers m and n, (ab)m = ambm. |
Example Simplify (-2ab2)3(a2)4.

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Exercises
Simplify each expression.1. (y5)2

2. (x2)5(x3)

3. -3(ab4)3

4. (-3ab4)3

5. (4a2)2(b3)

6. (-4xy)3(-2x2)3

7. (-3j2k3)2(2j2k)38. (25a 2b) 3 (15abf)2

9. (2x3y2z2)3(x2z)4

10. (-2n6y5)(-6n3y2)(ny)3

11. (-3a3n4)(-3a3n)4

12. -3(2x)4(4x5y)2