We will simplify the given expression step by step:

$(-x^5)^2$

Step 1: Apply the Power Rule

The power rule states that $(a^m)^n = a^{m \cdot n}$. Applying this to our expression:

$(-x^5)^2 = (-1 \cdot x^5)^2$

$= (-1)^2 \cdot (x^5)^2$

Step 2: Simplify Each Term

Since $(-1)^2 = 1$ and using the power rule again on $x^5$,

$(x^5)^2 = x^{5 \times 2} = x^{10}$

Thus, the final expression simplifies to:

$x^{10}$

Final Answer:

$x^{10}$

Would you like a further breakdown of any step?

Here are some related questions:

1. What is the power rule and how does it apply to exponents?
2. How do negative bases affect exponentiation?
3. What happens when an exponent is applied to a product of terms?
4. How do we simplify expressions with multiple exponentiation rules?
5. What is the difference between $(-x^5)^2$ and $-x^{10}$?

Tip: When raising a negative base to an even power, the result is always positive!