fraction with exponenets?

Question

36*a^8*b^4 times 1/2

over

27*a^9*B^6 times 1/3


do i subtract the exponent from top to bottom
or do i multipy first and then reduce or am i going in the wrong direction

Answer 1

What you want to do is factor out the same values from the numerator and denominators.

The order in which you factor these out does not matter, the key is to continue to factor them out until there is nothing else to factor out.

For example you can factor out a^8 by turning it into:

36 * (a^8) * (b^4) * 1/2
over
27 * (a^8) * a * (b^6) * 1/3

since (a^8) over (a^8) = 1 you can cancel them out leaving you with:

36 * (b^4) * 1/2
over
27 * a * (b^6) * 1/3

we do the same factoring for b where we can factor out a (b^4):

36 * (b^4) * 1/2
over
27 * a * (b^4) * (b^2) * 1/3

canceling the (b^4)s we get:

36 * 1/2
over
27 * a * (b^2) * 1/3

You can then further reduce the fraction by multiplying out the 36 * 1/2 and the 27 * 1/3: leaving you with:

18
over
9 * a * (b^2)

As you can see now you can factor out a multiple of 9 leaving you with:

2
over
a*b^2

Answer 2

You subtract the exponents ON the bottom FROM the top. That is:

[(1/2)(36 * a^8 * b^4)] / [(1/3)(27 * a^9 * b^6)]
= (18 * a^8 * b^4) / (9 * a^9 * b^6)
= 2 * a^(8-9) * b^(4-6)
= 2 * a^-1 * b^-2
= 2 / (ab²)

Answer 3

subtract exponents
(36/27)*a^(8-9)*b^(4-6)*(3/2)

after simplification:

2 / ( a*b^2 )

Answer 4

I'm not sure exactly what your saying, but I think you're right. Here's how you do it:

[36*a^8*b^4*(1/2)] / [27*a^9*b^6*(1/3)]

= [36*(1/2)] / [27*a*b^2*(1/3)]

= [18] / [9*a*b^2]

= 2 / ab^2

Answer 5

so we have 36 and change over two, and 27 and change over 3?

To divide, we multiply by the the reciprocal. So 36 and... over 2 times 3 over 27 and ...

Cross reduce, and then multiply

Answer 6

you can subtract bottom from top and if its a negative number that means it stays in the bottom and then multiply. it would be easier. this only means for like variables not numbers though

Answer 7

Ask a Math Teacher

Answer 8

(2)(1/ab^2)