Question

Write with positive exponents. Simplify: (1 / (p^(-(4/5))).

Answer 1

The expression
`1 / (p^(^-^(^4^/^5^))` with positive exponents simplifies to
`p^(^4^/^5^)`.

Step-by-step explanation:

In the given expression,
`1 / (p^(^-^(^4^/^5^))`, the negative exponent in the denominator can be transformed into a positive exponent by moving the entire term to the numerator. To do this, we reciprocate the base (p) and change the sign of the exponent. Thus, the expression becomes (
`p^(^4^/^5^)`).

Let's break down the steps for a clearer understanding:

1. Start with the original expression:
`1 / (p^(^-^(^4^/^5^))`

2. Reciprocate the base (p) and change the sign of the exponent:
`p^(^4^/^5^)`

3. The final answer is therefore
`p^(^4^/^5^)`.

This result indicates that the expression, when simplified with positive exponents, is equivalent to p raised to the power of 4/5. The positive exponent signifies that we are dealing with the reciprocal of the original base raised to the positive power, making the expression clearer and more concise.