The document discusses exponents and exponential expressions. It defines exponential expressions as involving a base number being multiplied by itself a certain number of times, called the exponent. It provides examples of exponential expressions and how they are read out loud. It also outlines some properties of exponential expressions, such as all powers of positive numbers being positive and the behavior of even and odd powers of negative numbers. Finally, it discusses like terms in exponential expressions and an identity property involving exponents.

2.  Exponents represent repeated multiplication.
For example,

3.  More generally, for any non-zero real number
a and for any whole number n,
In the exponential expression an, a is called
the base and n is called the exponent.

4.  a2 is read as ‘a squared’.
 a3 is read as ‘a cubed’.
 a4 is read as ‘a to the fourth power’.
...
 an is read as ‘a to the nth power’.

11. Homework.

14. Homework.

16. Homework.

18. Homework.

20. 1. All powers of a positive real number a are
positive, i.e. for a ∈ R, a > 0, and n ∈ Z,
an> 0.
2. The even powers of a negative real number
a are positive, i.e. for a ∈ R, a ≠ 0 and n ∈ Z,
(–a)n = an (if n is an even number).
3. The odd powers of a negative real number a
are negative, i.e. for a ∈ R, a ≠ 0 and n ∈ Z,
(–a)n= –an (if n is an odd number)

23. The terms of an expression which have the
same base and the same exponent are
called like terms. We can add or subtract
like terms.
(x ⋅ an) + (y ⋅ an) + (z ⋅ an) = (x + y + z) ⋅ an
(a ≠ 0)

25.  Let a ∈ R – {–1, 0, 1}
(a is a real number other than –1, 0
and 1).
If am = an then m = n.

26.  2x = 16
 3x+1 = 81
 22x + 1 = 8x – 1