Exponents: Printable Worksheets - Free Printable

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

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Part 1: Rewrite each expression using exponents

We are given repeated multiplication and need to rewrite it using exponent notation.

> Example:
> $ 7 \times 7 \times 7 \times 7 = 7^4 $

#### a. $ 6 \times 6 \times 6 \times 6 \times 6 $
- There are 5 sixes multiplied together.
- So, $ 6^5 $

✔ Answer: $ 6^5 $

#### b. $ 3 \times 3 \times 3 $
- Three 3s → $ 3^3 $

✔ Answer: $ 3^3 $

#### c. $ 2 \times 2 \times 2 \times 2 \times 2 \times 2 $
- Six 2s → $ 2^6 $

✔ Answer: $ 2^6 $

#### d. $ 9 \times 9 $
- Two 9s → $ 9^2 $

✔ Answer: $ 9^2 $

#### e. $ 31 \times 31 \times 31 \times 31 \times 31 $
- Five 31s → $ 31^5 $

✔ Answer: $ 31^5 $

#### f. $ 14 \times 14 \times 14 $
- Three 14s → $ 14^3 $

✔ Answer: $ 14^3 $

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Part 2: Rewrite each exponent in expanded form

We write the exponent as repeated multiplication.

> Example: $ 5^3 = 5 \times 5 \times 5 $

#### g. $ 8^4 $
- $ 8 \times 8 \times 8 \times 8 $

✔ Answer: $ 8 \times 8 \times 8 \times 8 $

#### h. $ 4^7 $
- Seven 4s multiplied: $ 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 $

✔ Answer: $ 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 $

#### i. $ 13^2 $
- $ 13 \times 13 $

✔ Answer: $ 13 \times 13 $

#### j. $ 100^3 $
- $ 100 \times 100 \times 100 $

✔ Answer: $ 100 \times 100 \times 100 $

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Part 3: Rewrite each exponent in standard form

Now we compute the actual value (multiply it out).

> Example: $ 4^3 = 216 $

Wait — actually, $ 4^3 = 4 \times 4 \times 4 = 64 $, so the example seems incorrect.

But let’s check:
$ 4^3 = 64 $, not 216.
$ 6^3 = 216 $. So likely a typo in the example.

But since the example says $ 4^3 = 216 $, that is wrong.

Let’s assume it's just an error and proceed correctly.

#### k. $ 5^3 $
- $ 5 \times 5 \times 5 = 125 $

✔ Answer: $ 125 $

#### l. $ 7^4 $
- $ 7 \times 7 \times 7 \times 7 $
- $ 7 \times 7 = 49 $
- $ 49 \times 7 = 343 $
- $ 343 \times 7 = 2401 $

✔ Answer: $ 2401 $

#### m. $ 4^3 $
- $ 4 \times 4 \times 4 = 64 $

✔ Answer: $ 64 $

#### n. $ 9^3 $
- $ 9 \times 9 \times 9 $
- $ 9 \times 9 = 81 $
- $ 81 \times 9 = 729 $

✔ Answer: $ 729 $

#### o. $ 1^3 $
- $ 1 \times 1 \times 1 = 1 $

✔ Answer: $ 1 $

#### p. $ 2^6 $
- $ 2 \times 2 \times 2 \times 2 \times 2 \times 2 $
- $ 2^2 = 4 $
- $ 2^4 = 16 $
- $ 2^6 = 64 $

✔ Answer: $ 64 $

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✔ Final Answers:

#### Part 1: Rewrite using exponents
a. $ 6^5 $
b. $ 3^3 $
c. $ 2^6 $
d. $ 9^2 $
e. $ 31^5 $
f. $ 14^3 $

#### Part 2: Expanded form
g. $ 8 \times 8 \times 8 \times 8 $
h. $ 4 \times 4 \times 4 \times 4 \times 4 \times 4 \times 4 $
i. $ 13 \times 13 $
j. $ 100 \times 100 \times 100 $

#### Part 3: Standard form
k. $ 125 $
l. $ 2401 $
m. $ 64 $
n. $ 729 $
o. $ 1 $
p. $ 64 $

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📌 Note:

The example in Part 3 says $ 4^3 = 216 $, which is incorrect.
Correctly: $ 4^3 = 64 $, and $ 6^3 = 216 $.
So the example should probably be $ 6^3 = 216 $, but it's written as $ 4^3 $, which is a mistake.

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