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?

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 #2

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 #3

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 #4

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 #5

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 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:

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,

Therefore, 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

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

Answer

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

Exercise #1

112= 11^2=

Video Solution

Answer

121

Exercise #2

62= 6^2=

Video Solution

Answer

36

Exercise #3

64= \sqrt{64}=

Video Solution

Answer

8

Exercise #4

36= \sqrt{36}=

Video Solution

Answer

6

Exercise #5

49= \sqrt{49}=

Video Solution

Answer

7

Exercise #1

Choose the largest value

Video Solution

Answer

25 \sqrt{25}

Exercise #2

Which of the following is equivalent to the expression below?

10,0001 10,000^1

Video Solution

Answer

10,0001 10,000\cdot1

Exercise #3

Choose the expression that is equal to the following:

27 2^7

Video Solution

Answer

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

Exercise #4

What is the missing exponent?

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

Video Solution

Answer

2

Exercise #5

121= \sqrt{121}=

Video Solution

Answer

11