🚌🚌Prime Factorization- Writing the Answer in Index Notation🚌🚌

Welcome 👦👧boys and girls to another class. Today, we will be going on an adventure where we will be exploring the topic: Prime Factorization-Writing the answer in Index Notation. Read all information carefully before writing your answers. Show all working. 

Prime Factorization is finding which prime numbers multiply together to make the original number.

Index Notation/Exponential Form) is a short way of writing a number multiplied by itself several times. Instead of writing 2 x 2 x 2 =
. The small number (3) is called the index or power. It tells us how many times to multiply the big number by itself. Examples👇

Examples:

Example 1: The number 12

• Step 1: $12=4\times 3$

• Step 2: $4=2\times 2$

• So, $12=2\times 2\times 3$

• Index Notation: Since there are two 2s, we write $2^2$.

• Answer: $12=2^2\times 3$

Example 2: The number 18

• Step 1: $18=6\times 3$

• Step 2: $6=2\times 3$

• So, $18=2\times 3\times 3$

• Index Notation: Since there are two 3s, we write $3^2$.

• Answer: $18=2\times 3^2$

Example 3: The number 72

• Step 1: $72=8\times 9$

• Step 2: $8=2\times 2\times 2$ and $9=3\times 3$

• So, $72=2\times 2\times 2\times 3\times 3$

• Index Notation: Three 2s = $2^3$. Two 3s = $3^2$.

• Answer: $72=2^3\times 3^2$

Task 1:

Write the correct answer in your notebook.

1. What is the prime factorization of 8?
   a) $4\times 2$
   b) $2^3$
   c) $2^2$
   d) $8^1$

2. What does $3^2$ mean?
   a) $3+3$
   b) $3\times 2$
   c) $3\times 3$
   d) $3\times 3\times 3$

3. What is the prime factorization of 27?
   a) $9\times 3$
   b) $3^3$
   c) $3^2$
   d) $2^3$

4. Write $2\times 2\times 5$ in index notation.
   a) $2^2\times 5$
   b) $2\times 5^2$
   c) $2^3\times 5$
   d) $20$

5. What is the prime factorization of 20?
   a) $4\times 5$
   b) $2^2\times 5$
   c) $2\times 5^2$
   d) $2^3\times 5$

6. Which number is a prime number?
   a) 9
   b) 15
   c) 7
   d) 21

7. What is the prime factorization of 36?
   a) $2^3\times 3$
   b) $2^2\times 3^2$
   c) $2\times 3^3$
   d) $6^2$

8. The index in $5^4$ is:
   a) 5
   b) 4
   c) 20
   d) 625

9. What is the prime factorization of 50?
   a) $2\times 5^2$
   b) $2^2\times 5$
   c) $5^2\times 2$
   d) Both A and C are correct

10. What is $2^3\times 3$ equal to?
    a) 12
    b) 18
    c) 24
    d) 36

11. Which is the correct prime factorization for 49?
    a) $7\times 7$
    b) $7^2$
    c) ${49}^1$
    d) Both A and B are correct

12. Write $3\times 3\times 3\times 2\times 2$ in index form.
    a) $3^3\times 2^2$
    b) $3^2\times 2^3$
    c) $3^3\times 2$
    d) $2^2\times 3^3$

13. What is the prime factorization of 100?
    a) $2^2\times 5^2$
    b) $2^3\times 5^2$
    c) ${10}^2$
    d) $2^2\times 5^3$

14. What is the missing factor? $2^3\times$ ____ $=24$
    a) 2
    b) 3
    c) 4
    d) 6

15. A number has the prime factorization $2^2\times 3\times 5$. What is the number?
    a) 30
    b) 45
    c) 60
    d) 75

Task 2: Write "True" or "False" for each statement.

1. $5^2$ is the same as $5\times 5$. __________

2. The prime factors of 15 are 3 and 5. __________

3. In index notation, the big number is called the "power". __________

4. $2\times 2\times 3$ can be written as $2^3\times 3$. __________

5. The prime factorization of 16 is $4^2$. __________

6. 11 is a prime number. __________

7. $3\times 3\times 3\times 3$ can be written as $3^4$. __________

8. The prime factorization of 45 is $3^2\times 5$. __________

9. 1 is a prime number. __________

10. $2^2\times 3^2=36$. __________ 

Task 3: Fill in the missing word or number to make the sentence correct.

1. $2\times 2\times 2=2^{\mathrm{\_}}$

2. The number 17 has only two factors: 1 and _____.

3. The prime factorization of 28 is $2^2\times$ _____.

4. In ${10}^3$, the index (power) is _____.

5. $7\times 7$ written in index notation is _____.

6. The prime factors of 10 are 2 and _____.

7. $3\times 3\times 5\times 5$ in index notation is $3^2\times$ _____.

8. The prime factorization of 32 is _____ (using index notation).

9. A number with only two factors (1 and itself) is called a _____ number.

10. $2\times$ _____ $\times 5=2^2\times 5$