# Help me evaluate this equation in Scientific Notation

How do i solve this using Scientific Notation? $$\frac{3\times 10^8}{4\times 10^{-5}}$$
I have been trying for hours now! Help please

• What is $3\div4$? What is $10^8\div10^{-5}$? – peterwhy Nov 11 '14 at 16:07
• If you've been trying for hours, the calculator might be of some use. I know that's usually not how we want to approach math but I think that it makes more sense to try that first than to post a question. – inkievoyd Nov 11 '14 at 16:07
• Scientific notation is significant figures I.e $0.01 = 1.00\times 10^{-2}$ to 3 significant figures. Does this help? – Chinny84 Nov 11 '14 at 16:12
• but for 10⁸÷10−⁵ do i only divide the indices? or all of it? – GeoGod Nov 11 '14 at 16:13

$$\dfrac {a^c}{a^d} = a^{c-d}$$
So your fraction is $$\frac{3\times 10^8}{4\times 10^{-5}} = \dfrac 34\times 10^{8 - (-5)} = \dfrac 34 \times 10^{13} = 0.75\times 10^{13}= 7.50 \times 10^{12}$$
First note that $$\frac{x^a}{x^{-b}}= \frac{x^a}{\frac{1}{x^{b}}}=x^ax^b =x^{a+b}, \quad x\not =0$$ So now $$\frac{3\times 10^8}{4\times 10^{-5}}= \frac{3}{4}\times \frac{10^8}{10^{-5}}= \frac{3}{4}\times 10^8\times 10^5$$ $$= 0.75\times 10^{8+5}= 0.75\times 10^{13}=7.5\times 10^{12}$$