Exponents and Multiplication worksheet for pre-algebra students, focusing on simplifying expressions with positive exponents.

Let’s solve each problem step by step. Remember: when multiplying terms with exponents, if the bases are the same, you add the exponents. Also, multiply the numbers (coefficients) first.

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1) 4² · 4²

Same base (4), so add exponents:
4^(2+2) = 4⁴
But we can also calculate it:
4² = 16, so 16 · 16 = 256
Or leave as 4⁴ — but since the problem says “simplify” and doesn’t specify form, either is fine. But let’s check instructions: “Your answer should contain only positive exponents.” So 4⁴ is acceptable. However, sometimes they want numerical value. Let’s see other problems — some have variables, so for pure numbers, maybe compute? Actually, looking at #2: 4·4² — that suggests they may expect simplified exponential form or number. Let’s do both ways and pick simplest.

Actually, in pre-algebra, often they want you to combine using exponent rules. So:

4² · 4² = 4^(2+2) = 4⁴ → which is 256, but 4⁴ has positive exponent, so okay. But let’s see what’s expected. Since #2 is 4·4², which is 4¹·4²=4³, probably they want exponential form unless it simplifies nicely.

Wait — actually, looking at all problems, many result in single term with coefficient and variable. For pure numbers, perhaps compute? Let me check standard practice. In Kuta worksheets like this, for #1 and #2, they usually expect numerical answer if no variables. Let me verify with calculation:

4² = 16, 16 × 16 = 256 → so 256

Similarly, #2: 4 · 4² = 4 × 16 = 64

So I think for pure numbers, compute the value.

But let’s confirm with exponent rule: 4²·4² = 4⁴ = 256 — same thing.

I’ll go with numerical value for pure number problems.

So:

1) 4² · 4² = 16 · 16 = 256

2) 4 · 4² = 4 · 16 = 64

(Alternatively, 4¹ · 4² = 4³ = 64)

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3) 3² · 3²

3² = 9, so 9 · 9 = 81
Or 3^(2+2)=3⁴=81

→ 81

4) 2 · 2² · 2²

First, 2 = 2¹, so total: 2¹ · 2² · 2² = 2^(1+2+2) = 2⁵ = 32
Or step by step: 2²=4, so 2 · 4 · 4 = 2·16=32

→ 32

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Now variables:

5) 2n⁴ · 5n⁴

Multiply coefficients: 2 · 5 = 10
Same base n, add exponents: n⁴ · n⁴ = n^(4+4) = n⁸
So: 10n⁸

6) 6r · 5r²

Coefficients: 6 · 5 = 30
Variables: r¹ · r² = r^(1+2) = r³
So: 30r³

7) 2n⁴ · 6n⁴

Coefficients: 2 · 6 = 12
Exponents: n⁴ · n = n⁸
→ 12n⁸

8) 6k² · k

k is k¹, so: 6 · 1 = 6 (coefficient)
k² · k¹ = k³
→ 6k³

9) 5b² · 8b

Coefficients: 5 · 8 = 40
b² · b¹ = b³
→ 40b³

10) 4x² · 3x

Coefficients: 4 · 3 = 12
x² · x¹ = x³
→ 12x³

11) 6x · 2x²

Coefficients: 6 · 2 = 12
x¹ · x² = x³
→ 12x³

12) 6x · 6x³

Coefficients: 6 · 6 = 36
x¹ · x³ = x⁴
→ 36x⁴

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Final Answers:

1) 256
2) 64
3) 81
4) 32
5) 10n⁸
6) 30r³
7) 12n⁸
8) 6k³
9) 40b³
10) 12x³
11) 12x³
12) 36x⁴

All answers have only positive exponents as required.

Final Answer:
1) 256
2) 64
3) 81
4) 32
5) 10n⁸
6) 30r³
7) 12n⁸
8) 6k³
9) 40b³
10) 12x³
11) 12x³
12) 36x⁴