Math Problem Statement

(5/3t^10)+(5/(3t)^10)

Solution

The given expression is:

53t10+5(3t)10\frac{5}{3}t^{10} + \frac{5}{(3t)^{10}}

Let's simplify this step-by-step.

  1. The first term, 53t10\frac{5}{3}t^{10}, remains unchanged because it's already simplified.

  2. For the second term, 5(3t)10\frac{5}{(3t)^{10}}, we need to expand the denominator: (3t)10=310t10(3t)^{10} = 3^{10} \cdot t^{10} So the second term becomes: 5310t10=559,049t10\frac{5}{3^{10} \cdot t^{10}} = \frac{5}{59,049 \cdot t^{10}}

Thus, the entire expression becomes:

53t10+559,049t10\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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Simplification

Formulas

Exponentiation of products: (ab)^n = a^n * b^n
Simplification of terms with exponents

Theorems

Laws of exponents: (a^m) / (a^n) = a^(m-n)
Distributive property of exponents over multiplication

Suitable Grade Level

Grades 9-10