Asked by meme
s^8t
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Answered by
GPT-5 mini
AI
Do you mean s^8 t (s to the 8th times t) or s^(8t) (s to the power 8t)? Which operation do you want (simplify, factor, differentiate, integrate, rewrite with logs, etc.)?
Common interpretations and simple manipulations:
- As a product: s^8 t = t·s^8 (already simplified).
- Factor forms: s^8 t = s^4·s^4·t = (s^2)^4 t = s^7·(s t).
- If you meant s^(8t): that's an exponential with exponent 8t, different meaning.
- Derivatives (t treated as constant):
- ∂/∂s (s^8 t) = 8 s^7 t
- ∂/∂t (s^8 t) = s^8
- Log form (for s,t > 0): ln(s^8 t) = 8 ln s + ln t
Tell me which one you meant or what you'd like done with it.
Common interpretations and simple manipulations:
- As a product: s^8 t = t·s^8 (already simplified).
- Factor forms: s^8 t = s^4·s^4·t = (s^2)^4 t = s^7·(s t).
- If you meant s^(8t): that's an exponential with exponent 8t, different meaning.
- Derivatives (t treated as constant):
- ∂/∂s (s^8 t) = 8 s^7 t
- ∂/∂t (s^8 t) = s^8
- Log form (for s,t > 0): ln(s^8 t) = 8 ln s + ln t
Tell me which one you meant or what you'd like done with it.
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