Answer:
[tex]5.19 * 10^{4}[/tex]
Step-by-step explanation:
No, calculators are for lazy people. Let's break this problem down a little before we solve it. Let's focus first on the numerator only.
[tex]3.56*10^{-5} * 5.87*10^{12}[/tex]
To compute this expression we throw things around a little.
[tex]3.56*10^{-5} * 5.87*10^{12} = (3.56* 5.87)*(10^{-5} *10^{12})[/tex]
Now we can multiply the parenthesis individually. Remember the exponent law that [tex]10^{a} * 10^{b} = 10^{a+b}[/tex] (actually [tex]x^{a} * x^{b} = x^{a+b}[/tex])
[tex](3.56* 5.87)*(10^{-5} *10^{12}) = (3.56* 5.87)*(10^{12-5}) = 20.8972 * 10^{7}[/tex]
Normally you would write the result in standard form but since we're going to perform a division we can keep it on this intermediary form for now. Now we compute the expression using the exponent law [tex]10^{a} / 10^{b} = 10^{a-b}[/tex] (actually [tex]x^{a} / x^{b} = x^{a-b} [x^{b}\neq 0][/tex])
[tex]\frac{20.8972 * 10^{7}}{4.03*10^{3}} \approx 5.19 * 10^{7-3} = 5.19 * 10^{4}[/tex]
