https://file.aiquickdraw.com/mathbot/file/1728405494913iin5re8a.jpg

The task in the image is to rewrite the fractions with negative exponents. Here’s how it is done:

### General Rule:
For any positive integer \( a \), \( \frac{1}{a^n} = a^{-n} \).

Let's apply this rule to each case:

**a)** \(\frac{1}{3^4} = 3^{-4}\)

**b)** \(\frac{1}{7^5} = 7^{-5}\)

**c)** \(\frac{1}{6^3} = 6^{-3}\)

**d)** \(\frac{1}{(-3)^2} = (-3)^{-2}\)

**e)** \(\frac{1}{2^1} = 2^{-1}\)

**f)** \(\frac{1}{-3} = (-3)^{-1}\)

**g)** \(\frac{1}{(-3)^3} = (-3)^{-3}\)

**h)** \(\frac{1}{27} = 27^{-1}\)  
(Note: \(27 = 3^3\), so it could also be written as \(3^{-3}\), but the question asks for the direct fraction form.)

**i)** \(\frac{1}{x^4} = x^{-4}\)

**j)** \(\frac{1}{3^7} = 3^{-7}\)

**k)** \(\frac{1}{(2y)^5} = (2y)^{-5}\)

**l)** \(\frac{1}{8a^3} = (8a^3)^{-1} = 8^{-1}a^{-3}\)  
(Note: \(8 = 2^3\), so it could also be written as \(2^{-3}a^{-3}\) if simplified.)

Would you like more details or explanations on any of these? 

Here are 5 related questions:
1. How do you simplify an expression with a negative exponent?
2. What happens if the base of a negative exponent is a fraction?
3. Can you explain how to rewrite expressions with both numbers and variables using negative exponents?
4. How would you approach simplifying fractional exponents?
5. How does distributing exponents over parentheses work?

**Tip**: Negative exponents indicate reciprocal operations—flipping the base to the denominator or numerator.

Rewrite the fraction with negative exponents.

Learn how to rewrite fractions with negative exponents using the rule 1/a^n = a^(-n). This problem involves exponents and is ideal for students in Grades 8-10.

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