This is gonna be tricky to write. What is a^-3 b^-8 over b^3 c^-4 ? Like simplified

Question

Pls show work! It would really help if u detailed this. I really have trouble with this one and finals are coming up and I really need to study and the YouTube lessons aren’t helping much. Answer before Friday pls. Or ASAP

Answer 1

Here is a vary important rule:

b^-3 = 1/b³

1/b^-3 = b³

That is, move variable between numerator and denominator and change the sign of the exponent.

a^-3b^-8 / b³c^-4

b^-8 / a³b³c^-4 [move a from numerator to denominator and change (-3) to (3)]

1 / b⁸a³b³c^-4 [move b to denominator]

1 / a³b¹¹c^-4 [combine b terms -- watch out for sign]

c⁴ / a³b¹¹ [simplified - could also be a^-3b^-11c⁴ ]

Answer 2

There are 2 rules in play here

1) When dividing terms with exponents we subtract so x^a/x^b = x^(a-b). So for example x^10/x^4 = x^(10-4) or x^6

2) a term raised to a negative power is 1/the term to the positive power or x^-a= 1/x^a or x^-3= 1/x^3

With this in mind lets look at your problem and its 3 variables

(a^-3)(b^-8)/ (b^3)((c^-4)

Lets look at the b terms (b^-8)/*b^3)= b^ (-8-3)= b^-11

this gives us (a^-3)(b^-11)/c^-4.

a^-3= 1/a^3 and b^-11= 1/b^11

so now have 1/(a^3)(b^11)(c^-4) but c^-4=1/c^4so this gives us

c^4/(a^3)(b^11)

Answer 3

Hi, the best way to understand exponents are to always make them positive. Example, if you had a^-2 in order to make the exponent positive you have to do its reciprocal (A.K.A. flip it) therefore you'll end up with 1/a^2.

Let's start with the numerator, you have a^-3 b^-8, to make their exponents positive you have to move them to the denominator. So now you have 1/a^3 b^8 b^3 c^-4. Since the only negative exponent left is c^-4 we have to make that positive, which if its in the denominator and we flip it, it'll move to the numerator. Now we have a problem that looks like c^4/a^3 b^8 b^3.

Moving to the basics of multiplying and dividing exponents, when you multiply you add the exponents when you divide you subtract. In our numerator, we have c^4, well we don't have any other c's in the numerator to add exponents or have any in the denominator to subtract, so the final exponent for c is 4. In our denominator, we'll start with a. There's no a's in the numerator or the denominator so our final exponent for a is 3. With b is a different story, so we don't have any b's in the numerator which means we won't be subtracting exponents, but we do have to exponents for b in the denominator. Since they are both in the same place of the fractions you are basically multiplying b^8*b^3, and when we multiply we add the exponents so the final exponent for b will be 11.

Now, let's put the answer together. in the numerator we have c^4 and in the denominator we have a^3 and b^11. Your answer will be c^4/a^3 b^11.

Feel free to message me if you have any other questions. Good Luck!

Answer 4

(a^-3b^-8)/(b³c^-4) = c⁴/(a³b⁸b³) Writing everything in terms of positive powers.

= c⁴/(a³b¹¹)