To simplify the expression \(\frac{1}{7}x^{-\frac{3}{5}}\), follow these steps:

1. Recognize the expression as a product of two terms: \(\frac{1}{7}\) and \(x^{-\frac{3}{5}}\).
2. Rewrite \(x^{-\frac{3}{5}}\) as \(\frac{1}{x^{\frac{3}{5}}}\) because a negative exponent indicates the reciprocal.

Putting these together, we have:
\[
\frac{1}{7}x^{-\frac{3}{5}} = \frac{1}{7} \cdot \frac{1}{x^{\frac{3}{5}}}
\]

Multiplying the fractions:
\[
\frac{1}{7} \cdot \frac{1}{x^{\frac{3}{5}}} = \frac{1}{7x^{\frac{3}{5}}}
\]

So, the simplified form of the expression is:
\[
\frac{1}{7x^{\frac{3}{5}}}
\]

Would you like more details on any of the steps? Do you have any questions?

Here are some related questions to expand on this topic:

1. How do you simplify expressions with negative exponents?
2. What is the general rule for converting negative exponents to positive exponents?
3. How do you handle division of variables with exponents?
4. Can you provide an example of simplifying a more complex expression with negative exponents?
5. What are the rules for multiplying and dividing exponents?
6. How do fractional exponents relate to roots?
7. How would the expression change if the exponent were positive instead?
8. How can you apply these rules to simplify expressions in calculus?

**Tip:** When dealing with exponents, always remember that a negative exponent signifies a reciprocal, and a fractional exponent represents a root.

Learn how to simplify the expression 1/7x^-3/5 with a detailed step-by-step guide. This problem covers key concepts in exponents, including negative exponents and fractional exponents. Suitable for high school students.

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