The given expression is:

\[
\frac{5}{3}t^{10} + \frac{5}{(3t)^{10}}
\]

Let's simplify this step-by-step.

1. The first term, \( \frac{5}{3}t^{10} \), remains unchanged because it's already simplified.
   
2. For the second term, \( \frac{5}{(3t)^{10}} \), we need to expand the denominator:
   \[
   (3t)^{10} = 3^{10} \cdot t^{10}
   \]
   So the second term becomes:
   \[
   \frac{5}{3^{10} \cdot t^{10}} = \frac{5}{59,049 \cdot t^{10}}
   \]

Thus, the entire expression becomes:

\[
\frac{5}{3}t^{10} + \frac{5}{59,049 t^{10}}
\]

There isn't any further simplification possible. This is the simplified form of the given expression.

Do you have any questions or would you like more details?

Here are 5 related questions:

1. How do you simplify exponents when variables and constants are combined?
2. How do fractional exponents work in expressions like this?
3. What are the properties of exponents when multiplying or dividing terms?
4. How would you handle exponents if the base includes both a variable and a constant?
5. Can you combine terms with different bases if they have the same exponent?

**Tip:** Always apply exponent rules carefully when the base is a product of terms. Each factor must be raised to the power separately.

This page provides a step-by-step solution for simplifying the algebraic expression (5/3t^10) + (5/(3t)^10). The solution covers key concepts such as the laws of exponents, the exponentiation of products, and simplification techniques. Suitable for students in Grades 9-10.

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