Prime factorization worksheet with exponents for educational practice.

Sure! Let’s solve each problem step by step. The goal is to find the prime factorization of each number and then write it in exponent form — that means grouping repeated prime factors using exponents.

---

a) 48 = 2·2·2·2·3 = 2⁴·3¹ ✔ (already done)

---

b) 80

Start dividing by smallest prime (2):

- 80 ÷ 2 = 40
- 40 ÷ 2 = 20
- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
- 5 is prime → stop.

So: 80 = 2·2·2·2·5 = 2⁴·5¹

---

c) 76

- 76 ÷ 2 = 38
- 38 ÷ 2 = 19
- 19 is prime.

So: 76 = 2·2·19 = 2²·19¹

---

d) 90

- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 is prime.

So: 90 = 2·3·3·5 = 2¹·3²·5¹

---

e) 20

- 20 ÷ 2 = 10
- 10 ÷ 2 = 5
- 5 is prime.

So: 20 = 2·2·5 = 2²·5¹

---

f) 32

This is a power of 2:

- 32 ÷ 2 = 16
- 16 ÷ 2 = 8
- 8 ÷ 2 = 4
- 4 ÷ 2 = 2
- 2 ÷ 2 = 1

So: 32 = 2·2·2·2·2 = 2⁵

---

g) 54

- 54 ÷ 2 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1

So: 54 = 2·3·3·3 = 2¹·3³

---

h) 88

- 88 ÷ 2 = 44
- 44 ÷ 2 = 22
- 22 ÷ 2 = 11
- 11 is prime.

So: 88 = 2·2·2·11 = 2³·11¹

---

i) 44

- 44 ÷ 2 = 22
- 22 ÷ 2 = 11
- 11 is prime.

So: 44 = 2·2·11 = 2²·11¹

---

j) 168

- 168 ÷ 2 = 84
- 84 ÷ 2 = 42
- 42 ÷ 2 = 21
- 21 ÷ 3 = 7
- 7 is prime.

So: 168 = 2·2·2·3·7 = 2³·3¹·7¹

---

k) 81

This is a power of 3:

- 81 ÷ 3 = 27
- 27 ÷ 3 = 9
- 9 ÷ 3 = 3
- 3 ÷ 3 = 1

So: 81 = 3·3·3·3 = 3⁴

---

l) 270

- 270 ÷ 2 = 135
- 135 ÷ 3 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 is prime.

So: 270 = 2·3·3·3·5 = 2¹·3³·5¹

---

## ✔ Final Answers:

b) 80 = 2⁴·5¹
c) 76 = 2²·19¹
d) 90 = 2¹·3²·5¹
e) 20 = 2²·5¹
f) 32 = 2⁵
g) 54 = 2¹·3³
h) 88 = 2³·11¹
i) 44 = 2²·11¹
j) 168 = 2³·3¹·7¹
k) 81 = 3⁴
l) 270 = 2¹·3³·5¹

Let me know if you’d like to see factor trees or more explanation for any of them!