Find the Domain 1/(p^-8)

Problem

1/(p(−8))

Solution

1. Rewrite the expression using the property of negative exponents, where a(−n)=1/(an)

p(−8)=1/(p8)

2. Substitute this back into the original expression to simplify the fraction.

1/1/(p8)=p8

3. Identify the constraints of the original expression. In the expression 1/(p(−8)) the term p(−8) is in the denominator.

p(−8)≠0

4. Analyze the term p(−8) Since p(−8)=1/(p8) the variable p is also in a denominator within that term.

p≠0

5. Determine the domain. Since p8 is defined for all real numbers but p cannot be zero due to the negative exponent (which places p in a denominator), the domain is all real numbers except zero.

Final Answer

Domain of 1/(p(−8))={[p∈ℝ,p≠0]}

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