Let's simplify the expression \((3f^{-2})^3\) step by step:
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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: \[ 3^3 \cdot (f^{-2})^3 = 27f^{-6} \]
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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
2 answers