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The expression you have is \((3^{-4})^7\), and you are asked to rewrite it using a single positive exponent.

We can solve this by applying the power of a power rule for exponents, which states:

\[
(a^m)^n = a^{m \cdot n}
\]

Here, the base is 3, the inner exponent is \(-4\), and the outer exponent is \(7\). Applying the rule:

\[
(3^{-4})^7 = 3^{-4 \cdot 7} = 3^{-28}
\]

Now, to express this using a positive exponent, we use the rule that \(a^{-m} = \frac{1}{a^m}\):

\[
3^{-28} = \frac{1}{3^{28}}
\]

So, the expression rewritten with a single positive exponent is:

\[
\frac{1}{3^{28}}
\]

Would you like more details or have any questions about the steps?

Here are 5 related questions:
1. How do you apply the product of powers rule to simplify expressions with exponents?
2. What happens when you multiply numbers with the same base but different exponents?
3. How would you simplify an expression like \((x^{-3})^5\)?
4. What is the difference between negative and positive exponents in terms of meaning?
5. Can you explain the rule for dividing powers with the same base?

**Tip**: When working with exponents, always remember to apply exponent rules step by step to avoid mistakes, especially when working with negative exponents.

Rewrite using a single positive exponent: (3^-4)^7

Learn how to rewrite the expression (3^-4)^7 using a single positive exponent. This solution involves applying the power of a power rule and the negative exponent rule. Suitable for students in Grade 8-10.

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