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