Find $w$, such that $5^65^w=25$.
The laws of exponents give us $5^65^w=5^{6+w}$.  And, because $25=5^2$, we have $5^{6+w}=5^2$.  It follows that $6+w=2$.  Subtracting 6 from both sides gives us $w=\boxed{-4}$.
-4
Level 1
Algebra
Problem: Find $w$, such that $5^65^w=25$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To solve for $w$, we start with the equation $5^6 \cdot 5^w = 25$. We recognize that $25$ can be expressed as a power of $5$. Specifically, $25 = 5^2$. 

Next, we apply the property of exponents that states $a^m \cdot a^n = a^{m+n}$. Using this property, we can combine the left side of the equation:

$5^6 \cdot 5^w = 5^{6+w}$.

Now, we can rewrite the equation as:

$5^{6+w} = 5^2$.

Since the bases are the same, we can set the exponents equal to each other:

$6 + w = 2$.

To isolate $w$, we subtract $6$ from both sides:

$w = 2 - 6$.

This simplifies to:

$w = -4$.

Thus, the final answer is $-4$.<|END_OF_LATENT|> The final answer is $-4$.