The expression \((4^3)^{-5}\) can be simplified step by step.

### Step 1: Simplify the exponent inside the parentheses
\[
4^3 = 64
\]
So the expression becomes:
\[
(64)^{-5}
\]

### Step 2: Apply the negative exponent rule
The negative exponent rule states that \(a^{-n} = \frac{1}{a^n}\). Applying this rule:
\[
64^{-5} = \frac{1}{64^5}
\]

### Step 3: Simplify \(64^5\)
\[
64^5 = 1073741824
\]

So the final answer is:
\[
(4^3)^{-5} = \frac{1}{1073741824}
\]

Would you like a further breakdown or clarification?

Here are 5 related questions to explore:
1. What is the result of \((3^2)^{-4}\)?
2. How do you simplify \((5^4)^3\)?
3. What happens if we apply a negative exponent rule to a fraction like \(\left(\frac{2}{3}\right)^{-2}\)?
4. How can you evaluate \((2^6)^{-3}\)?
5. What is the general rule for simplifying \((a^b)^c\)?

**Tip:** When dealing with negative exponents, remember that they signify taking the reciprocal of the base raised to the corresponding positive exponent.

Learn how to simplify the expression (4^3)^-5 step by step. This solution uses the negative exponent rule and the power of a power rule to calculate the final result. Suitable for students in Grades 8-10.

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