### Instruction: Find $w$, such that $5^65^w=25$.### Response: To solve for $w$, I need to express both sides of the equation in terms of the same base.
Since 25 is a power of 5, I can rewrite it as $5^2$.
Then, using the exponent rule $a^ba^c=a^{b+c}$, I can combine the exponents on the left side.
This gives me $5^{6+w}=5^2$.
Now, since the bases are equal, the exponents must also be equal.
So I can write $6+w=2$.
Solving for $w$, I get $w=2-6=-4$.