# Basis of a power - Examples, Exercises and Solutions

The base of the power is the number that is multiplied 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.

## examples with solutions for basis of a power

### Exercise #1

What is the answer to the following?

$3^2-3^3$

### 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 first calculate 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.

$-18$

### Exercise #2

Sovle:

$3^2+3^3$

### 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 first calculate 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.

36

### Exercise #3

Find the value of n:

$6^n=6\cdot6\cdot6$?

### Step-by-Step Solution

We use the formula: $a\times a=a^2$

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.

$n=3$

### Exercise #4

In the figure in front of you there are 3 squares

Write down the area of the shape in potential notation

### 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

$6^2+4^2+3^2$

### Exercise #5

$11^2=$

121

## examples with solutions for basis of a power

### Exercise #1

$6^2=$

36

### Exercise #2

Which of the following is equivalent to the expression below?

$10,000^1$

### Video Solution

$10,000\cdot1$

### Exercise #3

Choose the expression that is equal to the following:

$2^7$

### Video Solution

$2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2$

### Exercise #4

What is the missing exponent?

$-7^{\square}=-49$

2

### Exercise #5

$\sqrt{x}=1$

1

## examples with solutions for basis of a power

### Exercise #1

$\sqrt{x}=2$

4

### Exercise #2

$\sqrt{x}=6$

36

### Exercise #3

$7^3=$

### Video Solution

$343$

### Exercise #4

$5^3=$

### Video Solution

$125$

### Exercise #5

Which of the following clauses is equal to 100?

### Video Solution

$5^2\cdot2^2$