50+ product rule worksheets for 9th Grade on Quizizz | Free ... - Free Printable

Let's solve each of these problems step by step using the Exponent Product Rule, which states:

> When multiplying powers with the same base, add the exponents:
> $$
> a^m \cdot a^n = a^{m+n}
> $$

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1. Simplify: $ x^4 (x^{12}) $

We are multiplying two powers of $ x $:
$$
x^4 \cdot x^{12} = x^{4+12} = x^{16}
$$

✔ Answer: D) $ x^{16} $

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2. Simplify: $ 3^5 \cdot 3^7 $

Same base (3), so add exponents:
$$
3^5 \cdot 3^7 = 3^{5+7} = 3^{12}
$$

✔ Answer: C) $ 3^{12} $

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3. Simplify: $ n^2 \cdot n^4 $

Same base ($ n $), add exponents:
$$
n^2 \cdot n^4 = n^{2+4} = n^6
$$

✔ Answer: A) $ n^6 $

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4. Simplify: $ 5^2 \cdot 5 $

Note: $ 5 $ is the same as $ 5^1 $

So:
$$
5^2 \cdot 5^1 = 5^{2+1} = 5^3
$$

✔ Answer: A) $ 5^3 $

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5. Simplify: $ c^4 \cdot c^3 $

Same base ($ c $), add exponents:
$$
c^4 \cdot c^3 = c^{4+3} = c^7
$$

✔ Answer: B) $ c^7 $

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✔ Final Answers:

1. D
2. C
3. A
4. A
5. B

Let me know if you'd like help with the rest of the 20 questions!