# How do you write the answer in scientific notation given (1.2times10^-4)^2/((9.0times10^5)(1.6times10^-8))?

Oct 14, 2017

$1.0 \times {10}^{-} 6$

#### Explanation:

First we need to remember three properties of exponents:
1) ${\left(A \cdot B\right)}^{x} = {A}^{x} \cdot {B}^{x}$
2) ${A}^{-} x = \frac{1}{A} ^ x$
3) ${A}^{x} \cdot {A}^{y} = {A}^{x + y}$

Using the first property on the top leaves us with:
${1.2}^{2} \times {\left({10}^{-} 4\right)}^{2}$

Now, when you have an exponent raised to an exponent you multiply them, in this case getting ${10}^{-} 8$. Now our full equation looks like this:

$\frac{1.44 \times {10}^{-} 8}{\left(9.0 \times {10}^{5}\right) \times \left(1.6 \times {10}^{-} 8\right)}$

We can eliminate both ${10}^{-} 8$'s from the top and bottom:

$\frac{1.44}{\left(9.0 \times {10}^{5}\right) \times 1.6}$

If we divide top and bottom by 2, 4 times, we get:

$1.44 \div 2 = 0.72 \div 2 = 0.36 \div 2 = 0.18 \div 2 = 0.09 \text{ }$ on top

and

$1.6 \div 2 = 0.8 \div 2 = 0.4 \div 2 = 0.2 \div 2 = 0.1 \text{ }$ on the bottom,

leaving our equation like this:

$\frac{0.09}{\left(9.0 \times {10}^{5}\right) \times 0.1}$

Now, we divide $0.09$ by $0.1$ leaving us $0.9$ on top

$\frac{0.9}{9.0 \times {10}^{5}}$

Divide top and bottom by 9

$\frac{0.1}{1.0 \times {10}^{5}}$

$0.1$ can also be written as $1.0 \times {10}^{-} 1$

$\frac{1.0 \times {10}^{-} 1}{1.0 \times {10}^{5}}$

and using the second property we can write:

$\left(1.0 \times {10}^{-} 1\right) \times \left(1.0 \times {10}^{-} 5\right)$

Finally we can throw out the parenthesis and use the third property, adding the exponents on the 10's, leaving us with the final number:

$1.0 \times {10}^{-} 6$