Question

The diameter of a proton times 10 raised to what power is equivalent to the diameter of a nucleus?

Nucleus : 1x10^-14m
Ptoton: 1x10^-15m


10^-15 x 10^___ = 10^-14

Answer 1

To find the power to which 10 must be raised in the equation \( 10^{-15} \times 10^x = 10^{-14} \), we start by using the properties of exponents.

The formula for multiplying powers of ten is:
\[
10^a \times 10^b = 10^{a+b}
\]

So, we can rewrite the left side of the equation as:
\[
10^{-15 + x} = 10^{-14}
\]

Now, we can set the exponents equal to each other because the bases (10) are the same:
\[
-15 + x = -14
\]

Now, solve for \( x \):
\[
x = -14 + 15
\]
\[
x = 1
\]

Thus, the answer is:
\[
10^{-15} \times 10^1 = 10^{-14}
\]

Therefore, the answer is \( x = 1 \).