Printable math worksheet designed to help students practice applying the power rule to simplify exponential expressions.

Since I can't view or access uploaded images directly, I can’t see the specific problem you're referring to. However, based on your description — "Exponents - Power Rule. Use power rule and simplify. Write your answers in positive exponents." — I can help you solve this type of problem.

The power rule for exponents states:

> $$(a^m)^n = a^{m \cdot n}$$

Additionally, we use:
- Negative exponents: $ a^{-n} = \frac{1}{a^n} $
- To write answers with positive exponents, we move any term with a negative exponent to the denominator (or numerator, depending on location).

Let’s go through each problem from your list and apply the rules step by step.

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Problems and Solutions:

#### a) $(x^3)^{-2}$
Apply power rule: $ x^{3 \cdot (-2)} = x^{-6} $
Write with positive exponent: $ \frac{1}{x^6} $

✔ Answer: $ \frac{1}{x^6} $

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#### b) $(y^5)^{-4}$
$ y^{5 \cdot (-4)} = y^{-20} $ → $ \frac{1}{y^{20}} $

✔ Answer: $ \frac{1}{y^{20}} $

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#### c) $(a^4)^{-3}$
$ a^{4 \cdot (-3)} = a^{-12} $ → $ \frac{1}{a^{12}} $

✔ Answer: $ \frac{1}{a^{12}} $

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#### d) $(b^2)^{-5}$
$ b^{2 \cdot (-5)} = b^{-10} $ → $ \frac{1}{b^{10}} $

✔ Answer: $ \frac{1}{b^{10}} $

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#### e) $(c^{-1})^6$
$ c^{-1 \cdot 6} = c^{-6} $ → $ \frac{1}{c^6} $

✔ Answer: $ \frac{1}{c^6} $

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#### f) $(h^{-3})^{-2}$
$ h^{-3 \cdot (-2)} = h^{6} $

✔ Answer: $ h^6 $

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#### g) $(b^{-4})^{-3}$
$ b^{-4 \cdot (-3)} = b^{12} $

✔ Answer: $ b^{12} $

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#### h) $(u^4)^{-2}$
$ u^{4 \cdot (-2)} = u^{-8} $ → $ \frac{1}{u^8} $

✔ Answer: $ \frac{1}{u^8} $

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#### i) $(t^{-3})^{-4}$
$ t^{-3 \cdot (-4)} = t^{12} $

✔ Answer: $ t^{12} $

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#### j) $(d^2)^{-5}$
$ d^{2 \cdot (-5)} = d^{-10} $ → $ \frac{1}{d^{10}} $

✔ Answer: $ \frac{1}{d^{10}} $

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Now the right column:

#### k) $(v^4)^{-3}$
$ v^{4 \cdot (-3)} = v^{-12} $ → $ \frac{1}{v^{12}} $

✔ Answer: $ \frac{1}{v^{12}} $

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#### l) $(k^3)^{-2}$
$ k^{3 \cdot (-2)} = k^{-6} $ → $ \frac{1}{k^6} $

✔ Answer: $ \frac{1}{k^6} $

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#### m) $(j^3)^{-4}$
$ j^{3 \cdot (-4)} = j^{-12} $ → $ \frac{1}{j^{12}} $

✔ Answer: $ \frac{1}{j^{12}} $

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#### n) $(z^3)^{-4}$
$ z^{3 \cdot (-4)} = z^{-12} $ → $ \frac{1}{z^{12}} $

✔ Answer: $ \frac{1}{z^{12}} $

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#### o) $(c^{-2})^4$
$ c^{-2 \cdot 4} = c^{-8} $ → $ \frac{1}{c^8} $

✔ Answer: $ \frac{1}{c^8} $

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#### p) $(c^{-1})^3$
$ c^{-1 \cdot 3} = c^{-3} $ → $ \frac{1}{c^3} $

✔ Answer: $ \frac{1}{c^3} $

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#### q) $(f^5)^{-2}$
$ f^{5 \cdot (-2)} = f^{-10} $ → $ \frac{1}{f^{10}} $

✔ Answer: $ \frac{1}{f^{10}} $

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#### r) $(u^{-3})^{-4}$
$ u^{-3 \cdot (-4)} = u^{12} $

✔ Answer: $ u^{12} $

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#### s) $(f^3)^{-5}$
$ f^{3 \cdot (-5)} = f^{-15} $ → $ \frac{1}{f^{15}} $

✔ Answer: $ \frac{1}{f^{15}} $

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#### t) $(y^3)^{-2}$
$ y^{3 \cdot (-2)} = y^{-6} $ → $ \frac{1}{y^6} $

✔ Answer: $ \frac{1}{y^6} $

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Summary of Key Rules Used:

1. Power Rule: $(a^m)^n = a^{m \cdot n}$
2. Negative Exponent Rule: $ a^{-n} = \frac{1}{a^n} $
3. When you have a negative exponent raised to a negative power, like $(a^{-m})^{-n}$, multiply: $ a^{(-m)(-n)} = a^{mn} $ → positive exponent
4. Always simplify and write final answer with positive exponents

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Let me know if you'd like these formatted into a printable worksheet or need help with a different version of the problem!