SOLUTION: I need help with this problem: Write with positive exponents (3^-2 a^-2 b^5)over (c^-3 d^-4). Thanks

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: I need help with this problem: Write with positive exponents (3^-2 a^-2 b^5)over (c^-3 d^-4). Thanks       Log On


   



Question 262392: I need help with this problem:
Write with positive exponents (3^-2 a^-2 b^5)over (c^-3 d^-4).
Thanks



Found 4 solutions by drk, jim_thompson5910, richwmiller, Theo:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
here is the original question:
%283%5E%28-2%29%2Aa%5E%28-2%29%2Ab%5E5%29%2F+%28c%5E%28-3%29%2Ad%5E%28-4%29%29+
start with the numerator information:
move the 3 and a down to denominator, like this
%28b%5E5%29+%2F+%283%5E2%2Aa%5E2%2Ac%5E%28-3%29%2Ad%5E%28-4%29%29
Now move the c and d up to the numerator, like this
%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's break this up:

3%5E%28-2%29=1%2F3%5E2=1%2F9

a%5E%28-2%29=1%2Fa%5E2

c%5E%28-3%29=1%2Fc%5E3

d%5E%28-4%29=1%2Fd%5E4

-----------------------------------

So 3%5E%28-2%29a%5E%28-2%29b%5E5=%281%2F9%29%281%2Fa%5E2%29b%5E5=%28b%5E5%29%2F%289a%5E2%29

and c%5E%28-3%29d%5E%28-4%29=%281%2Fc%5E3%29%281%2Fd%5E4%29=1%2F%28c%5E3d%5E4%29


Altogether,


Now multiply by the reciprocal of the second fraction and simplify to get the final answer of %28b%5E5c%5E3d%5E4%29%2F%289a%5E2%29


So %283%5E%28-2%29a%5E%28-2%29b%5E5%29%2F%28c%5E%28-3%29d%5E%28-4%29%29 simplifies to %28b%5E5c%5E3d%5E4%29%2F%289a%5E2%29 where none of the variables can be equal to zero.


In other words,

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
This what you wrote
with spaces between terms.
%283%5E-2+a%5E-2+b%5E5%29%2F%28c%5E-3+d%5E-4%29
(3^-2 a^-2 b^5)/(c^-3 d^-4)
%283%5E%28-2%29%2A+a%5E%28-2+%29%2Ab%5E5%29%2F+%28c%5E%28-3%29%2Ad%5E%28-4%29%29
(3^(-2)* a^(-2)* b^5)/ (c^(-3)* d^(-4))
just flip those with negative exponents
%28c%5E%283%29%2A+d%5E%284+%29%2Ab%5E5%29%2F+%283%5E%282%29%2Aa%5E%282%29%29
(c^(3)* d^(4 )*b^5)/ (3^(2)*a^(2))

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your expression is:

%283%5E%28-2%29%2Aa%5E%28-2%29%2Ab%5E5%29%2F%28c%5E%28-3%29%2Ad%5E%28-4%29%29

in general, a%5E%28-b%29 = 1%2Fa%5Eb

your equation becomes:



this can be simplified to:

%28b%5E5%2F%283%5E2%2Aa%5E2%29%29%2F%281%2F%28c%5E3%2Ad%5E4%29%29

if we multiply this by %28c%5E3%2Ad%5E4%29%2F%28c%5E3%2Ad%5E4%29, we get:

%28%28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29%29%2F1%29 which becomes:

%28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29

we confirm by substituting values for a,b,c,d in both the original equation and the final equation to see if we get the same answer.

we will let:

a = 2
b = 3
c = 4
d = 5

original equation is:

%283%5E%28-2%29%2Aa%5E%28-2%29%2Ab%5E5%29%2F%28c%5E%28-3%29%2Ad%5E%28-4%29%29

substituting, this becomes:

%283%5E%28-2%29%2A2%5E%28-2%29%2A3%5E5%29%2F%284%5E%28-3%29%2A5%5E%28-4%29%29 = 270,000

final equation is:


%28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29

substituting, this becomes:


%28%283%5E5%2A4%5E3%2A5%5E4%29%2F%283%5E2%2A2%5E2%29%29 = 270,000

since they both equal the same value, the simplification is good.

your answer is:

%283%5E%28-2%29%2Aa%5E%28-2%29%2Ab%5E5%29%2F%28c%5E%28-3%29%2Ad%5E%28-4%29%29 becomes %28%28b%5E5%2Ac%5E3%2Ad%5E4%29%2F%283%5E2%2Aa%5E2%29%29