To simplify the expression $(-5)^2(-5)^6$ into a single power of the base, we use the product of powers rule:

$a^m \cdot a^n = a^{m+n}$

Here, the base is $-5$, and the exponents are $2$ and $6$. Adding the exponents:

$(-5)^2 \cdot (-5)^6 = (-5)^{2+6} = (-5)^8$

Final Answer:

$(-5)^8$

Would you like more explanation on the rule or further examples?

Related Questions:

1. How do you simplify expressions with different bases but similar exponents?
2. Can negative bases raised to even powers result in negative numbers?
3. How does the product of powers rule differ from the power of a power rule?
4. What happens when combining powers with coefficients in front of the base?
5. How would this change if one of the powers was negative?

Tip:

Always check whether the base is negative and whether the exponent is odd or even, as it affects the sign of the final result.