Fractions?????

Question

(b^2) ^-6
------------
b^-4

I have to solve this with positive exponets, how is that done?


THis division fraction problem is causing my trouble too.....

24m^4n^2 -8m^2n^3 + 4m^3n
--------------------------------------
4m^2n


Thank you for your help !!!

Answer 1

Knowing that a^-b = 1/(a^b) and that exponentiation of exponents is nothing else than multiplication of them, this problem is easy to solve.
First the top part:
(b^2)^-6=b^-12
Putting it together:
b^-12
-----
b^-4
Applying the first rule:
b^4
---------
b^12
Simplyfying:
1/(b^8) or b^-8

Since you needed positive exponentials. it is 1/(b^8)

The second problem:
24m^4n^2 - 8m^2n^3 + 4m^3n
------------------------------------------------
4m^2n

Making this little pieces and simplifying each piece:

24m^4n^2
---------------- = 6m^2n
4m^2n

8m^2n^3
--------------- = 2n^2
4m^2n

4m^3n
---------- = m
4m^2n

Putting it back together:

6mn - 2n^2 + m

Answer 2

Problem 1: Multiply the exponents in the numerator... your fraction look like this when you do:
b^-12 / b^-4.
We know that we can invert a value with a negative exponent to make it a positive exponent. Doing this gives us the complex fraction of:

1/b^12
______
1/b^4

Simplifying this means to invert the denominator and multiply the fractions, thusly:
1/b^12 x b^4/1
Which yields:
b^12 / b^4
To divide these values, we subtract the exponents...
b^(12 - 4)
Giving us the final solution:
b^8

Problem 2 is a long division problem... although we can simplify each portion of the problem first, by rewriting as 3 separate fractions:
(24m^4 n^2) / (4m^2 n) - (8m^2 n^3) / (4m^2 n) + (4m^3 n) / (4m^2 n)

Simplify each fraction:
(6m^2 n) / 1 - (2n^2) / 1 + m/1
Clean up the denominators:
6m^2n - 2n^2 + m

Answer 3

For problem #2 the answer is 6m^2n-2n^2+m. As for 1st problem get the reciprocal of that to get a positive exponent:
b^4
----- = b^-8
b^12
So the answer is 1/b^8

Answer 4

Here's problem 1:
= b ^ -12 / b^-4
= b ^(-12 - (-4))
= b ^ -8 = 1/(b^8)

For problem 2, I'll give you a hint: Try factoring out the greatest common factor and seeing if anything cancels ?? :) Good luck!

Answer 5

b^-4 in the denominator is the same as b^4 in the numerator.

[(b^2) - 6] * b^4

distributive law:

b^6 - 6*b^4

Answer 6

(b^2) ^-6
------------
b^-4

b^{(2 * -6) - (-4)} = b^{-12+4} = b^-8

if you want to change it into positif equation so the answer is 1/b^8

24m^4n^2 -8m^2n^3 + 4m^3n
------------------------------...
4m^2n

you have to divide the nominator and denominator by 4 :

6m^4n^2 -2m^2n^3 + m^3n
------------------------------...
m^2n

6m^(2*4)n -2m^(3*2)n + m^3n
------------------------------...
m^2n

6m^8n -2m^6n + m^3n
------------------------------...
m^2n

then you start with the power : (denominator and nominator divided by m^2n

6m^(8n-2n) - 2m^(6n-2n) + m^(3n-2n)
= 6m^6n - 2m^4n + m^n
= m^n (6m^5n - 2m^3n + 1)