What is the quotient of 8x10^24 / 2x10^18 in scientific notation?

2. First, you must divide the coefficients ([tex]\frac{8}{2}=4[/tex]) and then, you must divide the power of 10, to do this you must substract the exponents 24 and 18 ([tex]24-18=6[/tex]). Therefore, you obtain the following result:

[tex]\frac{(8)(10^{24})}{(2)(10^{18})}=(4)(10^{6})[/tex]

The answer is: [tex](4)(10^{6})[/tex]

lhannearaujo lhannearaujo · Answer 2 · 2022-04-01T16:46:21+02:00

The quotient for given the algebraic expression, in scientific notation, is [tex]4*10^6[/tex].

Main Simplify Rules

For solving this question, it is necessary to apply Simplify Rules. Then, you should:

Apply the factoring or factorization for writing an algebraic expression in factors from common terms and if it's possible to eliminate them;
Apply the main power rules for simplifying the exponents;

From factoring rules, you can rewrite the given question as:

[tex]\frac{8 * 10^{24}}{2 * 10^{18}} =\frac{2 (4 * 10^{24})}{2 * 10^{18}} =\frac{4 * 10^{24}}{ 10^{18}}[/tex]

In the previous step, the common term, 2, was eliminated.

After that, you should apply the power rules - quotient of exponentials with same base.This rule indicates that when you take the quotient of two exponentials with the same base, the exponents should be subtracted.

Therefore, for [tex]\frac{10^{24}}{10^{18}}[/tex] you should repeat the base (10) and subtract the exponents (24-18=6). Then, you will have [tex]10^6[/tex]

Thus, [tex]\frac{4 * 10^{24}}{ 10^{18}}=4 *10^6[/tex].