# Powers and roots - Examples, Exercises and Solutions

## Exponents and Roots

### What is an exponent?

Exponentiation is the requirement for the number to be multiplied by itself several times.

### What is a root?

A root is the inverse operation of exponentiation, which helps us discover which number multiplied by itself gives this result.

The square root is equal to the power of 0.5.

## Practice Powers and roots

### 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

$\sqrt{441}=$

### Step-by-Step Solution

The root of 441 is 21.

$21\times21=$

$21\times20+21=$

$420+21=441$

$21$

### Exercise #4

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 #5

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 #1

$11^2=$

121

### Exercise #2

$6^2=$

36

### Exercise #3

$\sqrt{64}=$

8

### Exercise #4

$\sqrt{36}=$

6

### Exercise #5

$\sqrt{49}=$

7

### Exercise #1

Choose the largest value

### Video Solution

$\sqrt{25}$

### 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?

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

### Video Solution

$\sqrt{121}=$