https://file.aiquickdraw.com/mathbot/file/1728258646050kmgu59le.jpg

The problem in the image is:

\[
\frac{2t}{(t^{-4})(2t)}
\]

### Step 1: Simplify the denominator
The denominator is \( (t^{-4})(2t) \). We can first combine the terms with the same base \( t \).

\[
t^{-4} \cdot t = t^{-4 + 1} = t^{-3}
\]

So, the denominator becomes \( 2t^{-3} \).

### Step 2: Simplify the entire expression
Now the expression becomes:

\[
\frac{2t}{2t^{-3}}
\]

Cancel the common factor of 2 from both numerator and denominator:

\[
\frac{t}{t^{-3}}
\]

### Step 3: Use the rule of exponents
When dividing powers of the same base, subtract the exponents:

\[
t^{1 - (-3)} = t^{1 + 3} = t^4
\]

### Final Answer:
\[
t^4
\]

The simplified expression is \( t^4 \), with all exponents in positive form.

Do you need more details or have any questions?

Here are 5 related questions:
1. What is the rule for multiplying terms with the same base?
2. How do you divide powers with the same base?
3. How do negative exponents work in expressions?
4. Can you explain how to cancel terms in a fraction like this?
5. What would happen if the exponents were already positive?

**Tip:** When dividing exponents with the same base, always remember to subtract the exponent in the denominator from the exponent in the numerator.

Simplify: 2t / (t^(-4) * 2t), expressing the answer using positive exponents.

Learn how to simplify the expression 2t / (t^(-4) * 2t) using exponent rules, including negative exponents and division of powers. This step-by-step guide covers key algebraic concepts suitable for students in Grades 8-10.

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