To find the power to which 10 should be raised to make the diameter of a proton equivalent to the diameter of a nucleus, we can set up the relationship using the given diameters.
- Diameter of a Proton: \( 1 \times 10^{-15} \) meters
- Diameter of a Nucleus: \( 1 \times 10^{-14} \) meters
To find the power of 10, we can divide the diameter of a nucleus by the diameter of a proton:
\[ \frac{1 \times 10^{-14}}{1 \times 10^{-15}} = 10^{(-14) - (-15)} = 10^{1} \]
Thus, the diameter of a proton multiplied by \( 10^{1} \) gives us the diameter of a nucleus.
Therefore, the answer is:
1 (the diameter of a proton times \( 10^1 \) equals the diameter of a nucleus).