The base of the power is the number that ismultiplied by itself as many times as indicated by the exponent. The base appears as a number or algebraic expression. In its upper right corner, the exponent is shown in small.

The base of the power has to stand out clearly since it is the base!

The base of the power can be positive or negative and, depending on the exponent, the sign in the result will be modified.

When the base of the power is a positive number and the exponent is an even number the result will be positive.

Even when the base of the power is a positive number and the exponent is an odd number, the result will also be positive.

Even when the base of the power is a negative number and the exponent is an even number, the result will be positive.

When the base of the power is a negative number and the exponent is odd, the result will be negative.

The base of the power is the number that is multiplied by itself as many times as indicated by the exponent.

How can you remember it? It is called base because the power is raised on it: it is our base. If the power has no base, then there is no power. How can we identify the base of the power? The base of the power will appear as a number or algebraic expression. In its upper right corner we can see, in small, the exponent. The base of the power has to stand out clearly since it is the base! Let's see it in the following example: $a^2$ What is the base of the power? Of course a! The base on which we raise the power is a. In this example the exponent asks a, the base of the power, to multiply by itself twice. That is: $a\times a$ We can say that: $a^2=a\times a$

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In the formula, we see that the power shows the number of terms that are multiplied, that is, two times

Since in the exercise we multiply 6 three times, it means that we have 3 terms.

Therefore, the power, which is n in this case, will be 3.

Answer

$n=3$

Exercise #2

What is the answer to the following?

$3^2-3^3$

Video Solution

Step-by-Step Solution

Remember that according to the order of operations, exponents come before multiplication and division, which come before addition and subtraction (and parentheses always before everything),

So firstcalculate the values of the terms in the power and then subtract between the results:

$3^2-3^3 =9-27=-18$Therefore, the correct answer is option A.

Answer

$-18$

Exercise #3

Sovle:

$3^2+3^3$

Video Solution

Step-by-Step Solution

Remember that according to the order of operations, exponents precede multiplication and division, which precede addition and subtraction (and parentheses always precede everything).

So firstcalculate the values of the terms in the power and then subtract between the results:

$3^2+3^3 =9+27=36$Therefore, the correct answer is option B.

Answer

36

Exercise #4

In the figure in front of you there are 3 squares

Write down the area of the shape in potential notation

Video Solution

Step-by-Step Solution

Using the formula for the area of a square whose side is b:

$S=b^2$In the problem of the drawing, three squares whose sides have a length: 6, 3, and 4, units of length from left to right in the drawing respectively,

Therefore the areas are:

$S_1=3^2,\hspace{4pt}S_2=6^2,\hspace{4pt}S_3=4^2$square units respectively,

Therefore, the total area of the shape, composed of the three squares, is as follows:

$S_{\text{total}}=S_1+S_2+S_3=3^2+6^2+4^2$square units

Therefore, we recognize through the substitution property in addition that the correct answer is answer C.