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The given expression to simplify is:

\[
\frac{-5m^{-5}}{-3(m^{-5})^4}
\]

Let's simplify this step-by-step while ensuring all exponents are positive.

### Step 1: Simplify the expression inside the denominator
The denominator has \((m^{-5})^4\). Apply the power rule, \((a^m)^n = a^{mn}\):

\[
(m^{-5})^4 = m^{-20}
\]

So, the expression becomes:

\[
\frac{-5m^{-5}}{-3m^{-20}}
\]

### Step 2: Combine the terms
The negative signs cancel each other out, so we can rewrite the fraction without them:

\[
\frac{5m^{-5}}{3m^{-20}}
\]

### Step 3: Apply the division rule for exponents
When dividing terms with the same base, subtract the exponents:

\[
m^{-5} \div m^{-20} = m^{-5 - (-20)} = m^{-5 + 20} = m^{15}
\]

So, the expression simplifies to:

\[
\frac{5}{3} \cdot m^{15}
\]

### Step 4: Write the final answer with positive exponents
Since \(m^{15}\) already has a positive exponent, the final simplified form is:

\[
\frac{5m^{15}}{3}
\]

### Final Answer
The simplified expression in terms of only positive exponents is:

\[
\frac{5m^{15}}{3}
\]

Would you like further details, or do you have any questions?

### Related Questions:
1. How do you multiply expressions with exponents?
2. What is the power rule for exponents, and how is it applied?
3. How do you handle negative exponents in a fraction?
4. What is the general method for simplifying expressions with multiple exponents?
5. How do you convert between fractional exponents and radicals?

### Tip:
Always remember to combine like terms carefully, and watch out for the rules concerning negative exponents and division.

Express the following fraction in simplest form, only using positive exponents: -5m^(-5) / -3(m^(-5))^4

Learn how to simplify the exponential expression -5m^(-5) / -3(m^(-5))^4 using positive exponents. This solution covers exponent rules, including the power and division rules. Suitable for high school students in Grades 9-11.

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