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/(a^n)

p^(−8)=1/(p^8)

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

1/1/(p^8)=p^8

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/(p^8) the variable p is also in a denominator within that term.

p≠0

5. Determine the domain. Since p^8 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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