Developing Exponent Rules
Multiplication
By expanding the expression, then re-combining you can simplify the expression.
Example 1:
x6 x2 = ( x  x  x  x  x  x) (x  x) = x8 ; because there are a total of 8 x’s.
Example 2:
y3 y4 = (y  y  y) (y  y  y  y) = y7 ; because there are a total of 7 y’s.
Example 3:
(m2 n4 ) (mn2 ) = (m  m  n  n  n  n) (m  n  n) = m3 n6 ; because there are a total of 3 m's and
6 n's.
Simplify the following expressions by expanding each part:
1. y6 y2 =
2. x3 x =
3. r2 r3 =
4. m5 m4 =
5. (m3 n)(m3 n2) =
6. (y5 z2)(y2 z) =
7. (k2 m5 )(km) =
8. Can you find a pattern for what is happening with the exponents? What is the pattern, or
rule?
9. Use your rule from #8 to solve the following:
a.
y12 y8 =
b.
t15 t21 =
c.
(y13 z12)(y22 z10) =
10. In your own words, write the rule for exponents when multiplying.
11. Constants Rule: Treat the constants (regular #s) the way the operation tells you to
treat them.
Example: 7x5 ● 8x2 = 7●8= 56
x5+2 =
Now You Try These:
1.
114 ● 113 =
2.
53 ● 56 =
3.
x ● x2 ● x4=
4.
a ● b ● a2 =
And these:
1.
2y3 ● 7x2 ● 3y4 =
2. 3m2 ● 2n3 ● 7m3 =
Tonight’s Homework:
Complete Worksheet problems # 1 - 16
56x7