50+ Properties of Exponents worksheets on Quizizz | Free & Printable - Free Printable

Let's solve each of the four questions step by step, using the division properties of exponents and other relevant exponent rules.

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Question 1: Simplify

$$
\frac{t^5 u^4}{t^2 u}
$$

Step-by-step:

We apply the rule:
$$
\frac{a^m}{a^n} = a^{m-n}
$$

For $ t $: $ t^5 / t^2 = t^{5-2} = t^3 $

For $ u $: $ u^4 / u = u^{4-1} = u^3 $

So:
$$
\frac{t^5 u^4}{t^2 u} = t^3 u^3
$$

✔ Answer: A) $ t^3 u^3 $

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Question 2: Simplify

$$
\left( \frac{2a^3 b^5}{3} \right)^2
$$

We apply the power of a quotient rule:
$$
\left( \frac{a}{b} \right)^n = \frac{a^n}{b^n}
$$

So:
$$
\left( \frac{2a^3 b^5}{3} \right)^2 = \frac{(2a^3 b^5)^2}{3^2} = \frac{2^2 (a^3)^2 (b^5)^2}{9}
$$

Now simplify:
- $ 2^2 = 4 $
- $ (a^3)^2 = a^6 $
- $ (b^5)^2 = b^{10} $

So:
$$
\frac{4a^6 b^{10}}{9}
$$

✔ Answer: C) $ \frac{4a^6 b^{10}}{9} $

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Question 3: Simplify

$$
\left( \frac{3f^4 g h^4}{32 f^3 g^4 h} \right)^0
$$

Any non-zero expression raised to the power of 0 is 1.

But let’s confirm that the base is not zero. The expression inside is a fraction with variables, but unless specified otherwise, we assume variables are non-zero.

So:
$$
(\text{anything})^0 = 1 \quad \text{(as long as the base ≠ 0)}
$$

✔ Answer: C) 1

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Question 4: Simplify

$$
\frac{x^{-4} y^9}{z^{-2}}
$$

We use negative exponent rules:
- $ x^{-n} = \frac{1}{x^n} $
- So $ x^{-4} = \frac{1}{x^4} $
- $ z^{-2} = \frac{1}{z^2} $

So rewrite:
$$
\frac{\frac{1}{x^4} \cdot y^9}{\frac{1}{z^2}} = \frac{y^9}{x^4} \div \frac{1}{z^2} = \frac{y^9}{x^4} \cdot z^2 = \frac{z^2 y^9}{x^4}
$$

Alternatively, move negative exponents to denominator or numerator:

- $ x^{-4} $ in numerator → move to denominator as $ x^4 $
- $ z^{-2} $ in denominator → move to numerator as $ z^2 $

So:
$$
\frac{x^{-4} y^9}{z^{-2}} = \frac{y^9 z^2}{x^4}
$$

Which is:
$$
\frac{z^2 y^9}{x^4}
$$

✔ Answer: C) $ \frac{z^2 y^9}{x^4} $

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✔ Final Answers:

1. A
2. C
3. C
4. C

Let me know if you'd like this explained in another way!