Questions: Simplify the expression, rewriting without parenthesis or negative exponent [ left(frac2 z p^-2aright)^4= ]

Solution Steps

To simplify the given expression, we need to follow these steps:

1. Distribute the exponent to each term inside the parentheses.
2. Simplify the resulting expression by handling the negative exponent.

We start with the expression

\[ \left(\frac{2 z p^{-2}}{a}\right)^{4} \]

Applying the exponent to each term inside the parentheses, we have:

\[ \frac{(2^{4})(z^{4})(p^{-2 \cdot 4})}{(a^{4})} = \frac{16 z^{4} p^{-8}}{a^{4}} \]

Next, we simplify the expression by rewriting the term with the negative exponent:

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

Thus, the expression becomes:

\[ \frac{16 z^{4}}{a^{4} p^{8}} \]

Final Answer