# How do you evaluate ((5.0 g cm ^-3) (520 times 10^-10 cm)^3 (6.022 times 10^23 mol ^-1)) / (104 g mol^ -1)?

Sep 17, 2017

Well you could write it properly first. And I realize the formatting on this board is not wholly intuitive.....

#### Explanation:

We gots......

$\frac{5.0 \cdot g \cdot c {m}^{-} 3 \times {\left(520 \times {10}^{-} 10 \cdot c m\right)}^{3} \times 6.022 \times {10}^{23} \cdot m o {l}^{-} 1}{104 \cdot g \cdot m o {l}^{-} 1}$

And then we cancel out the units to get a dimensionless answer....

$\frac{5.0 \cdot \cancel{g \cdot c {m}^{-} 3} \times {520}^{3} \times {10}^{-} 30 \cdot \cancel{c {m}^{3}} \times 6.022 \times {10}^{23} \cdot \cancel{m o {l}^{-} 1}}{104 \cdot \cancel{g \cdot m o {l}^{-} 1}}$

$\cong 4$

Did I get it right? All care taken but no responsibility admitted.