Simplify. Assume all variables are positive.
t
5

2
t
1

3
Write your answer in the form A or 
A

B
, where A and B are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.


To simplify the given expression, let’s first clarify the expression from your description:

It seems that you are referring to a fraction with terms involving \( t \) and possibly other constants, but the exact form is unclear. Let's assume it could look something like this based on the structure you provided:

\[
\frac{t^5}{2t^1} \times 3
\]

If this is correct, we can proceed with the simplification.

### Step-by-Step Solution

1. **Interpret and Rewrite the Expression**:
   \[
   \frac{t^5}{2t} \times 3
   \]

2. **Simplify the Terms with \( t \)**:
   In the fraction \( \frac{t^5}{t} \), apply the rule of exponents \( \frac{a^m}{a^n} = a^{m-n} \):
   \[
   t^5 / t = t^{5 - 1} = t^4
   \]
   So, the expression now becomes:
   \[
   \frac{t^4}{2} \times 3
   \]

3. **Multiply by 3**:
   Distribute the 3 over the fraction:
   \[
   \frac{3 \cdot t^4}{2} = \frac{3t^4}{2}
   \]

### Final Answer
The simplified form is:
\[
\frac{3t^4}{2}
\]

This answer is in the form \(\frac{A}{B}\), where \( A = 3t^4 \) and \( B = 2 \), with all exponents positive.

Would you like further details or have any questions?

### Related Questions
1. How would the answer change if the exponent in the numerator was different?
2. How do you simplify expressions with multiple variables?
3. Can you explain the rules for dividing exponents with the same base?
4. What happens if there is a negative exponent in the fraction?
5. How would you approach simplifying if \( t \) had different coefficients?

**Tip**: When simplifying expressions with exponents, always apply exponent rules carefully and simplify constants separately.

Simplify. Assume all variables are positive. t^5 / (2 * t^1) * 3. Write your answer in the form A or A/B, where A and B are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

Simplify the algebraic expression t^5 / (2 * t) * 3, using exponent rules and expressing the answer in the form A/B with all positive exponents. This guide covers exponent division and multiplication, ideal for students in Grades 8-10.

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