Exponents and Powers interactive worksheet - Free Printable

Let's solve the Exponents Worksheet step by step and explain each part.

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🔹 Part 1: Rewrite using repeated multiplication and solve

We are given expressions with exponents. The exponent tells us how many times to multiply the base by itself.

#### Example:
> $ 3^2 = 3 \times 3 = 9 $

Now, let’s solve each:

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1) $ 4^2 = 4 \times 4 = \boxed{16} $

2) $ 2^5 = 2 \times 2 \times 2 \times 2 \times 2 = \boxed{32} $

3) $ 3^3 = 3 \times 3 \times 3 = \boxed{27} $

4) $ 5^1 = 5 = \boxed{5} $
*(Any number to the power of 1 is itself)*

5) $ 7^3 = 7 \times 7 \times 7 = 49 \times 7 = \boxed{343} $

6) $ 8^3 = 8 \times 8 \times 8 = 64 \times 8 = \boxed{512} $

7) $ 4^4 = 4 \times 4 \times 4 \times 4 = 16 \times 16 = \boxed{256} $

8) $ 10^2 = 10 \times 10 = \boxed{100} $

9) $ 12^2 = 12 \times 12 = \boxed{144} $

10) $ 6^4 = 6 \times 6 \times 6 \times 6 = 36 \times 36 = \boxed{1296} $

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🔹 Part 2: Rewrite the following expressions using exponents

We need to express repeated multiplication as a base raised to an exponent.

#### Example:
> $ 5 \times 5 = 5^2 $

Now solve each:

11) $ 8 \times 8 \times 8 = \boxed{8^3} $

12) $ 7 \times 7 \times 7 = \boxed{7^3} $

13) $ 6 \times 6 \times 6 \times 6 \times 6 = \boxed{6^5} $

14) $ 5 \times 5 \times 5 = \boxed{5^3} $

15) $ 2 \times 2 \times 2 \times 2 = \boxed{2^4} $

16) $ 10 \times 10 = \boxed{10^2} $

17) $ 6 \times 6 \times 6 \times 6 \times 6 = \boxed{6^5} $

18) $ 3 \times 3 \times 3 \times 3 = \boxed{3^4} $

19) $ 4 \times 4 \times 4 = \boxed{4^3} $

20) $ 7 \times 7 \times 7 \times 7 \times 7 = \boxed{7^5} $

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✔ Final Answers:

#### Part 1 (Evaluate):
1) 16
2) 32
3) 27
4) 5
5) 343
6) 512
7) 256
8) 100
9) 144
10) 1296

#### Part 2 (Rewrite using exponents):
11) $ 8^3 $
12) $ 7^3 $
13) $ 6^5 $
14) $ 5^3 $
15) $ 2^4 $
16) $ 10^2 $
17) $ 6^5 $
18) $ 3^4 $
19) $ 4^3 $
20) $ 7^5 $

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📌 Key Concepts Recap:

- Base: The number being multiplied (e.g., in $ 4^3 $, base is 4).
- Exponent: How many times the base is used as a factor (e.g., in $ 4^3 $, it means 4 × 4 × 4).
- Repeated multiplication → Exponent form: Count how many times the same number appears.
- Exponent → Repeated multiplication: Write the base multiplied by itself that many times.

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