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Exponent Rules and Multiplying Monomials5.45.4
1. Multiply monomials.2. Multiply numbers in scientific notation.3. Simplify a monomial raised to a power.
Objective 1
Multiply monomials.
23 • 24
43 2 2
7 2
23 means three 2s.
24 means four 2s.
Since there are a total of seven 2s multiplied, we can express the product as 27.
Keep the base and add the exponents
222 2222
Product Rule for ExponentsIf a is a real number and m and n are integers, then am • an = am+n.
When an equation in one variable is solved the answer is a point on a line.
Multiply:Multiply:
52 99
62 44
64 33
54 33
79 103
84 84 93 93
Multiplying Monomials 1. Multiply coefficients. 2. Add the exponents of the like bases. 3. Write any unlike variable bases unchanged
in the product.
853 1472 aaa
When an equation in one variable is solved the answer is a point on a line.
Simplify:Simplify:
23 75 xx
33 52 xx
42 35
33 52 xx
532
32
65
41
knkmmk
535x 20258125
610x 37x
nmk 48
365
Objective 2
Multiply numbers in scientific notation.
Monomials: Scientific notation:
3 6 3 6
9
4 10 2 10 4 2 10
8 10
9
6363
8
2424
a
aaa
When an equation in one variable is solved the answer is a point on a line.
Multiply and write result in scientific notation:Multiply and write result in scientific notation:
3 44.5 10 5.7 10
3 66.2 10 3.1 10
7106525 .
8105652 .
3102219 .2109221 .
Objective 3
Simplify a monomial raised to a power.
52x 22222 xxxxx 10x
A Power Raised to a PowerIf a is a real number and m and n are integers, then (am)n = amn.
34a aaa 444 334 a 364a
Raising a Product to a PowerIf a and b are real numbers and n is an integer, then (ab)n = anbn.
Simplifying a Monomial Raised to a Power
1. Evaluate the coefficient raised to that power.
2. Multiply each variable’s exponent by the power.
8128124423 1622 yxyxyx
When an equation in one variable is solved the answer is a point on a line.
Simplify:Simplify:
2323 yx
22yx
5322 yx
523yx
649 yx 15102 yx
24yx 1015yx
When an equation in one variable is solved the answer is a point on a line.
Simplify:Simplify:
3242 22 xyyx
543243 yzzyx
232325 yxyx
633484 22 yxyx
101110117 1282 yxyx
205361233 zyzyx
2311122311123 273 zyxzyx
64615 yxyx
1219yx
Slide 5- 17Copyright © 2011 Pearson Education, Inc.
Simplify.
a)
b)
c)
d)
7 36 3b b
2118b
1018b
219b
109b
5.4
Slide 5- 18Copyright © 2011 Pearson Education, Inc.
Simplify.
a)
b)
c)
d)
7 36 3b b
2118b
1018b
219b
109b
5.4
Slide 5- 19Copyright © 2011 Pearson Education, Inc.
Simplify.
a)
b)
c)
d)
42 34 5y y
920y
2020y
92500y
142500y
5.4
Slide 5- 20Copyright © 2011 Pearson Education, Inc.
Simplify.
a)
b)
c)
d)
42 34 5y y
920y
2020y
92500y
142500y
5.4
