Study the box below. Follow the directions and write the answer in the space provided.
Rule:
An exponent tells the number of times
a base is multiplied by itself.
-exponent
9.9.9.9= 94
-base
Examples:
43 = 4.4.4 Expanded form
2.4.2.4 = 22.42 Exponential form
52 = 25
Simplified
Write each problem in expanded form.
1. 78
3. x
5. 89.9
2. 45
4. al.ba
6. 22.35

[tex]7^8 = 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7[/tex].
[tex]4^5 = 4 \times 4 \times 4 \times 4 \times 4[/tex].
[tex]x^3 = x \times x \times x[/tex].
[tex]a^2 \cdot b^2 = a \times a \times b \times b[/tex].
[tex]8^9 \cdot 9 = 8 \times 8 \times 8 \times 8\times 8 \times 8 \times 8 \times 8 \times 8 \times 9[/tex].
[tex]2^2 \cdot 3^5 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3[/tex].

The exponent of a number or an expression is used to expand the expression.

Take for instance, the following expression in its exponential form

[tex]3^2[/tex]

The above expression means that, the value of 3 multiplied twice

The first expression is given as 7^8.

This represents the value of 7 multiplied by itself 8 times.

So, we have:

[tex]7^8 = 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7 \times 7[/tex]

Using the above as a guide, the expanded forms of the other expressions are:

[tex]4^5 = 4 \times 4 \times 4 \times 4 \times 4[/tex].
[tex]x^3 = x \times x \times x[/tex].
[tex]a^2 \cdot b^2 = a \times a \times b \times b[/tex].
[tex]8^9 \cdot 9 = 8 \times 8 \times 8 \times 8\times 8 \times 8 \times 8 \times 8 \times 8 \times 9[/tex].
[tex]2^2 \cdot 3^5 = 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3[/tex].