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Which expressions can be simplified as StartFraction 1 Over p Superscript 16 EndFraction? Check all that apply.

(p-4)4
(p8)-2
(p0)-16
(p16)-1
(p-2)-8

1 answer

To determine which expressions can be simplified to \( \frac{1}{p^{16}} \), we will simplify each expression one by one.

  1. \((p-4)^4\): This expression cannot be simplified to \( \frac{1}{p^{16}} \). The base is not \( p \) but \( p-4 \), so it does not match.

  2. \((p^8)^{-2}\): \[ (p^8)^{-2} = p^{-16} \] This can be rewritten as: \[ \frac{1}{p^{16}} \] This matches \( \frac{1}{p^{16}} \).

  3. \((p^0)^{-16}\): Since \( p^0 = 1 \), \[ (p^0)^{-16} = 1^{-16} = 1 \] This does not match \( \frac{1}{p^{16}} \).

  4. \((p^{16})^{-1}\): \[ (p^{16})^{-1} = p^{-16} \] This can be rewritten as: \[ \frac{1}{p^{16}} \] This matches \( \frac{1}{p^{16}} \).

  5. \((p^{-2})^{-8}\): \[ (p^{-2})^{-8} = p^{16} \] This does not match \( \frac{1}{p^{16}} \).

Now, summarizing the findings:

The expressions that can be simplified to \( \frac{1}{p^{16}} \) are:

  • \((p^8)^{-2}\)
  • \((p^{16})^{-1}\)

So, the correct answers are:

  • \((p^8)^{-2}\)
  • \((p^{16})^{-1}\)