Page 93 - MarceAlgebra Demystified

80 CHAPTER 5 Exponents and Roots

Examples

3 4 3 3 6 3 6 3 2 y 7 7 3 4
¼ ¼ 3 ¼ y ¼ y
3 2 6 3 6 3 y 3
n m
Property 3 (a ) ¼ a nm

If you have a quantity raised to a power then raised to another power,
multiply the exponents.

Examples

3 2 2 6 6 7 ð6Þð7Þ 42
ð5 Þ ¼ð5 5 5Þ ¼ð5 5 5Þð5 5 5Þ¼ 5 ðx Þ ¼ x ¼ x
Be careful, Properties 1 and 3 are easily confused.

0
Property 4 a =1

Any nonzero number raised to the zero power is one. We will see that this is
true by Property 2 and the fact that any nonzero number over itself is one.
16 4 2 2 2 0 0
1 ¼ ¼ ¼ 4 ¼ 4 From this we can see that 4 must be 1.
16 4 2

Practice

Rewrite using a single exponent.
x 8
1: ¼
x 2
3 2
2: ðx Þ ¼

7 3
3: y y ¼
10
4: x x ¼

x 3
5: ¼
x 2
5 5
6: ðy Þ ¼