Question

Simplify. Assume all variables (-s)⁻¹/⁵ Write your answer in the forn that have no variables in com

Answer 1

To simplify (-s)⁻¹/⁵, take the reciprocal of -s due to the negative exponent, then apply the fifth root because of the fractional exponent ⁻¹/⁵, resulting in the fifth root of the reciprocal of -s. No further simplification is possible, so the final answer is √[5]{1/(-s)}.

Step-by-step explanation:

To simplify the expression (-s)⁻¹/⁵, we need to understand the properties of exponents. A negative exponent indicates a reciprocal, and a fractional exponent indicates a root. So, (-s)⁻¹/⁵ is the fifth root of the reciprocal of -s.

Here's the step-by-step simplification:

1. First, recognize the negative exponent means to take the reciprocal: 1/(-s).
2. Next, apply the fractional exponent: ⁻¹/⁵ means the fifth root, so the expression becomes √[5]{1/(-s)}.
3. Eliminate terms wherever possible, but in this case, there are no further simplifications.
4. Finally, check the expression to ensure it is reasonable and follows all rules of exponents and roots.

The final simplified result is therefore √[5]{1/(-s)}, and since no terms can be eliminated to further simplify the expression, this is the simplified subscript.

Remember, when working with exponents and roots, it can be useful to recall constants like 5-6-7-8 with the minus sign to keep track of sign changes.