Question

Express the following fraction in simplest form, only using positive exponents.
start fraction, 4, p, to the power minus 8 , divided by, minus, 4, left parenthesis, p, to the power minus 2 , right parenthesis, to the power 4 , end fraction
−4(p
−2
)
4

4p
−8

​

Answer 1

To simplify the fraction

\[
\frac{4p^{-8}}{-4(p^{-2})^4},
\]

we start by simplifying the denominator.

1. Simplify \((p^{-2})^4\):
\[
(p^{-2})^4 = p^{-8}.
\]

2. Substitute this back into the denominator:
\[
-4(p^{-2})^4 = -4p^{-8}.
\]

Now, we rewrite the fraction:

\[
\frac{4p^{-8}}{-4p^{-8}}.
\]

3. Calculate the fraction:
\[
\frac{4}{-4} = -1 \quad \text{and} \quad \frac{p^{-8}}{p^{-8}} = 1.
\]

Thus, we have:

\[
\frac{4p^{-8}}{-4p^{-8}} = -1.
\]

Therefore, the simplified form of the given fraction is:

\[
-1.
\]