Question

Simplify the expression to have only one positive exponent.

(3f−2)3


Question 2
To simplify the expression you apply the
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rule to distribute the exponent
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to both terms.
Question 3
The
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rule is applied to the
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term by moving the variable to the
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.

Answer 1

Let's simplify the expression \((3f^{-2})^3\) step by step:

1. **Distributing the exponent**:
To simplify this expression, we'll apply the **power of a product rule**, which states that \((ab)^n = a^n b^n\). In this case, we can distribute the exponent \(3\) to both \(3\) and \(f^{-2}\):

\[
(3f^{-2})^3 = 3^3 \cdot (f^{-2})^3
\]

Now we calculate each component:
- \(3^3 = 27\)
- \((f^{-2})^3 = f^{-6}\) (using the power of a power rule, which states that \((a^m)^n = a^{m \cdot n}\))

Therefore, we have:
\[
3^3 \cdot (f^{-2})^3 = 27f^{-6}
\]

2. **Writing with positive exponents**:
The expression \(27f^{-6}\) can be rewritten to have only positive exponents. We do this by moving the variable \(f\) from the denominator to the numerator:
\[
27f^{-6} = \frac{27}{f^6}
\]

Now, let's answer your questions based on this process:

**Question 2:** To simplify the expression you apply the **power of a product** rule to distribute the exponent **3** to both terms.

**Question 3:** The **power of a power** rule is applied to the **\(f^{-2}\)** term by moving the variable to the **denominator**.

So the final answers are:
- Question 2: power of a product
- Question 3: power of a power; \(f^{-2}\); denominator