# Question #0bf56

Jun 7, 2017

See explanation below.

#### Explanation:

You need to get ${Q}_{2}$ by itself.
First, write 280,000 in scientific notation:

$2.8 \cdot {10}^{5} = 1.12 \cdot {10}^{8} \cdot \frac{1 \cdot {10}^{-} 4 \cdot {Q}_{2}}{{0.01}^{2}}$

Rewrite $0.0001$ as $1 \cdot {10}^{-} 4$ then cancel out the like terms:

$2.8 \cdot {10}^{5} = 1.12 \cdot {10}^{8} \cdot \frac{1 \cdot {10}^{-} 4 \cdot {Q}_{2}}{1 \cdot {10}^{-} 4}$

$2.8 \cdot {10}^{5} = 1.12 \cdot {10}^{8} \cdot {Q}_{2}$

Divide both sides by $1.12 \cdot {10}^{8}$

$\frac{2.8 \cdot {10}^{5}}{1.12 \cdot {10}^{8}} = {Q}_{2}$

Break up the left hand side and apply this index law:

$\frac{a \cdot {10}^{x}}{b \cdot {10}^{y}} = \left(\frac{a}{b}\right) \cdot {10}^{x - y}$

${Q}_{2} = \left(\frac{2.8}{1.12}\right) \cdot \left({10}^{5} / {10}^{8}\right) = \left(2.5\right) \cdot {10}^{5 - 8}$

${Q}_{2} = 2.5 \cdot {10}^{-} 3$