https://file.aiquickdraw.com/mathbot/file/1726163915105r9sm9cig.jpg

The expression provided is:

\[
\frac{1}{4p^{-4}}
\]

We are asked to rewrite the expression without using negative exponents.

### Step 1: Eliminate the negative exponent
We know the rule for negative exponents: 
\[
a^{-n} = \frac{1}{a^n}
\]
Thus, applying this rule to the term \( p^{-4} \):

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

So the entire expression becomes:

\[
\frac{1}{4 \cdot \frac{1}{p^4}} = \frac{1}{\frac{4}{p^4}} 
\]

### Step 2: Simplify the fraction
Dividing by a fraction is the same as multiplying by its reciprocal. Therefore:

\[
\frac{1}{\frac{4}{p^4}} = \frac{1 \cdot p^4}{4} = \frac{p^4}{4}
\]

### Final Simplified Expression:
\[
\frac{p^4}{4}
\]

Thus, the expression without negative exponents and fully simplified is:

\[
\boxed{\frac{p^4}{4}}
\]

Would you like further details or have any other questions?

### Relative Questions:
1. How do you simplify expressions with multiple negative exponents?
2. What are the properties of exponents used in simplifying algebraic expressions?
3. How do you multiply and divide terms with exponents?
4. Can you explain the difference between negative and fractional exponents?
5. How do you simplify expressions with variables raised to negative exponents?

### Tip:
When working with negative exponents, remember that they indicate reciprocals. This makes it easier to rewrite expressions in a simplified form.

Rewrite the expression 1 / (4p^-4) without using a negative exponent, and simplify it as much as possible.

Learn how to simplify the expression 1 / 4p^-4 by eliminating the negative exponent. This problem covers the properties of exponents and algebraic simplification. Suitable for students in Grades 8-10.

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