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.