To solve the given mathematical expression [tex]\(\frac{-1}{3 t^3} + e^{5x} + 7\)[/tex], let's break it down step by step.
1. Identify the Components: The expression comprises three main parts:
- [tex]\(\frac{-1}{3 t^3}\)[/tex]
- [tex]\(e^{5x}\)[/tex]
- [tex]\(7\)[/tex]
2. Simplify Each Part:
- [tex]\(\frac{-1}{3 t^3}\)[/tex] represents the fraction [tex]\(\frac{1}{3 t^3}\)[/tex] with a negative sign. This term involves the variable [tex]\(t\)[/tex] raised to the power of 3 and then taken the reciprocal.
- [tex]\(e^{5x}\)[/tex] represents the exponential function with base [tex]\(e\)[/tex] (Euler's number) raised to the power of [tex]\(5x\)[/tex]. This term depends on the variable [tex]\(x\)[/tex].
- [tex]\(7\)[/tex] is a constant term.
3. Combine the Terms:
After simplifying individual parts, combine them back to form the complete expression:
[tex]\[
\frac{-1}{3 t^3} + e^{5x} + 7
\][/tex]
4. Re-express the Components:
To ensure the expression is clear and fully simplified, rewrite it as:
[tex]\[
-\frac{1}{3 t^3} + e^{5x} + 7
\][/tex]
5. Final Expression:
The combined and simplified answer to the expression is:
[tex]\[
e^{5x} + 7 - \frac{1}{3 t^3}
\][/tex]
This is the fully simplified form of the given mathematical expression [tex]\(\frac{-1}{3 t^3} + e^{5 x} + 7\)[/tex].
