Question

moles of Cu in 5.0*10^21 atoms of Cu

Answer 1

That dozen-apple analogy would work here as well:
If I have 12 apples, then I have a dozen apples.
If I have 36 apples, then I have 36/12 = 3 dozens of apples.
Going from somethings to a dozen somethings, we will always divide by 12.

For moles, we basically replace 12 with 6.022*10^23 and apples with Cu atoms.
If I have 5.0*10^21 Cu atoms, then I have 5.0*10^21/(6.022*10^23) moles of Cu.. Or if unit conversions help see the underlying math:
\( \# \ \text{atoms} \times \dfrac{1 \ \text{mole}}{6.022*10^{23} \ \text{atoms}} = \# \ \text{moles} \)

Answer 2

I did follow this method but for some reason it wont take my answer. My answer was 8.3*10^43 mole

Answer 3

The issue seems to be the 10^43. When you divide exponents, you would subtract the numerator's power from the denominator's power. so 10^21 / 10^23 = 10^(21-23) = 10^-2.

Answer 4

The Answer turned out to be 8.3*10^-3

Answer 5

Sounds good. 5.0 / 6.022 = 0.83. 10^(21-23) = 10^-2.
0.83 * 10^-2 = 8.3 * 10^-3

Answer 6

Makes sense thank you again! Does that rule only apply when u divide?

Answer 7

Correct. When you divide the exponents with the same base, you subtract the two powers. When you multiply the two, they are added.

The algebra looks like this:
\(10^a * 10^b = 10^{a+b} \)
\( \dfrac{10^a}{10^b} = 10^{a} *10^{\color{red}{-b}} = 10^{a\color{red}{-b}} \)