Exponents and Roots

What is an exponent?

An exponent tells us the amount of times a number is to be multiplied by itself.

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.

Exponents and the Base of the Exponents

Practice Powers and Roots - Basic

Examples with solutions for Powers and Roots - Basic

Exercise #1

Choose the largest value

Video Solution

Step-by-Step Solution

Let's begin by calculating the numerical value of each of the roots in the given options:

25=516=49=3 \sqrt{25}=5\\ \sqrt{16}=4\\ \sqrt{9}=3\\ We can determine that:

5>4>3>1 Therefore, the correct answer is option A

Answer

25 \sqrt{25}

Exercise #2

Find the value of n:

6n=666 6^n=6\cdot6\cdot6 ?

Video Solution

Step-by-Step Solution

We use the formula: a×a=a2 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.

Answer

n=3 n=3

Exercise #3

Sovle:

32+33 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 first calculate the values of the terms in the power and then subtract between the results:

32+33=9+27=36 3^2+3^3 =9+27=36 Therefore, the correct answer is option B.

Answer

36

Exercise #4

441= \sqrt{441}=

Video Solution

Step-by-Step Solution

The root of 441 is 21.

21×21= 21\times21=

21×20+21= 21\times20+21=

420+21=441 420+21=441

Answer

21 21

Exercise #5

What is the answer to the following?

3233 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 first calculate the values of the terms in the power and then subtract between the results:

3233=927=18 3^2-3^3 =9-27=-18 Therefore, the correct answer is option A.

Answer

18 -18

Exercise #6

(380.2512)211= (\sqrt{380.25}-\frac{1}{2})^2-11=

Video Solution

Step-by-Step Solution

According to the order of operations, we should first solve the expression inside of the parentheses:

(380.2512)=(19.512)=(19) (\sqrt{380.25}-\frac{1}{2})=(19.5-\frac{1}{2})=(19)

In the next step, we will proceed to solve the exponentiation, and finally the subtraction:

(19)211=(19×19)11=36111=350 (19)^2-11=(19\times19)-11=361-11=350

Answer

350

Exercise #7

In the figure in front of you there are 3 squares

Write down the area of the shape in potential notation

333666444

Video Solution

Step-by-Step Solution

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

S=b2 S=b^2 In the picture, we are presented with three squares whose sides from left to right have a length of 6, 3, and 4 respectively:

Therefore the areas are:

S1=32,S2=62,S3=42 S_1=3^2,\hspace{4pt}S_2=6^2,\hspace{4pt}S_3=4^2 square units respectively,

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

Stotal=S1+S2+S3=32+62+42 S_{\text{total}}=S_1+S_2+S_3=3^2+6^2+4^2 square units

To conclude, we recognise through the rules of substitution and addition that the correct answer is answer C.

Answer

62+42+32 6^2+4^2+3^2

Exercise #8

Choose the expression that is equal to the following:

27 2^7

Video Solution

Answer

2222222 2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2

Exercise #9

112= 11^2=

Video Solution

Answer

121

Exercise #10

62= 6^2=

Video Solution

Answer

36

Exercise #11

36= \sqrt{36}=

Video Solution

Answer

6

Exercise #12

49= \sqrt{49}=

Video Solution

Answer

7

Exercise #13

64= \sqrt{64}=

Video Solution

Answer

8

Exercise #14

What is the missing exponent?

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

Video Solution

Answer

2

Exercise #15

Which of the following is equivalent to the expression below?

10,0001 10,000^1

Video Solution

Answer

10,0001 10,000\cdot1