Simplify 3p^0 / 3p. Express your answer using positive exponents.
Understand the Problem
The question is asking to simplify the expression 3p^0 / 3p, focusing on using positive exponents for the final answer.
Answer
$$ \frac{1}{p} $$
Answer for screen readers
$$ \frac{1}{p} $$
Steps to Solve
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Evaluate ( p^0 ) The expression ( p^0 ) is equal to 1 for any non-zero value of ( p ). Therefore, we can rewrite the numerator: $$ 3p^0 = 3 \cdot 1 = 3 $$
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Rewrite the fraction Now substitute ( 3p^0 ) in the fraction: $$ \frac{3p^0}{3p} = \frac{3}{3p} $$
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Simplify the fraction The ( 3 ) in the numerator and the ( 3 ) in the denominator cancel out: $$ \frac{3}{3p} = \frac{1}{p} $$
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Express with positive exponent The final answer does not require exponents less than one since ( \frac{1}{p} ) can be rewritten as ( p^{-1} ). However, since the question asks for positive exponents, we maintain it as ( \frac{1}{p} ).
$$ \frac{1}{p} $$
More Information
This simplification shows that when dividing expressions with exponents, it's essential to remember the properties of exponents, particularly that any variable to the power of zero equals one.
Tips
- Forgetting that ( p^0 = 1 ) and thus simplifying incorrectly.
- Not recognizing that ( 3 ) cancels out, leading to an incorrect fraction.
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