### Instruction: If $2^{10} \cdot 2^{15}$ is expressed as some integer to the fifth power, what is that integer?### Response: So we have $2^{10} * 2^{15}$.
If we add the exponents together, we get $2^{25}$.
Right, so $2^{10} * 2^{15} = 2^{25}$.
But we want to express $2^{25}$ as some integer to the fifth power.
So we want to find some integer $x$ such that $x^5 = 2^{25}$.
Right. So we can write $x^5$ as $2^{5x}$
And we have $2^{5x} = 2^{25}$.
So $5x=25$.
And $x=5$.