Exponents

Objective: To write and simplify expressions involving exponents.

The number 16 can be written as 4 ×4 or 5² and is called a power of 4. It is can also be written as 2⁴ because it is also 2 ×2 ×2 ×2.

In 2⁴, the little 4 is called the exponent and the normal 2 is called the base.

Exponents can either be positive, negative or zero. Any number except 0 raised to the 0 power is 1. In general, if a, and n are real numbers then

an= a ×a ×a &timees;�×a n times

Numbers can be written in either exponential form or in standard form. For example the number 25 in standard form can be written as 5 ×5 in exponential form.

Here the number 4 is written to positive, zero, and negative exponents

64, 16, 4, 1, 1 4 , 1 16 , 1 64 , 1 256 , �

which can be written as

43, 42, 41, 40, 4-1, 4-2, 4-3, 4-4, �

Exponents can also be fractions a number x^a/b where a and b are integers.

Simplify each expression in exponential form.

(1) 2 ·2 ·2 ·2

(2) x ·x ·x ·x ·x ·x

(3) n ·y ·y ·n

(4) x ·y ·y

(5) k ·5 ·2 ·k·k

(6) 3 ·u ·u ·2 ·u ·u

(7) -r ·-r

(8) f ·g ·g ·f

(9) y·y ·y ·z ·z ·y

(10) -3 ·a ·-2 ·a ·a ·a

(11) s·t ·t ·t ·s

(12) m ·2 ·n ·m ·n ·m ·n

Simplify.

(13) 34

(14) 43

(15) 5 ·32

(16) (3·2)3

(17) (-3)4

(18) -43

(19) (3 + 2)2

(20) 3+ 22