Question

With the restriction x ≠ 0, Which of the following is the simplified form of 6 times x to the ninth power over 4 times x to the fourth power times the fraction 12 times x squared over 3 times x to the fifth power ?

6 over x squared
6x8
6 over x to the eighth power
6x2

Answer 1

@dumbcow @ganeshie8 can you guys help me?

Answer 2

@mathmate

Answer 3

can you write it using numbers/symbols ?

Answer 4

kk give me a sec ;)

Answer 5

\[(6x^9)/(4x^4) * (12x^2)/(3x^5) \] with restriction of \[x \neq0\]

Answer 6

\[\huge \dfrac{6x^9}{4x^4} \times \dfrac{12x^2}{3x^5}\]

Answer 7

like that ?

Answer 8

yes, I sorry I don't know how to use latex format ;)

Answer 9

Multiplying fractions is easy -
you just multiply numerators separately
and denominators separately

Answer 10

\[\huge \dfrac{6x^9\times 12x^2}{4x^4\times 3x^5} \]

Answer 11

I'm not sure how to do the restriction part

Answer 12

forget about the restriction, for now

Answer 13

it is only saying that x cannot equal 0 as it would make the expression undefined

Answer 14

you get 6x^2

Answer 15

Yep !and the restriction carries along : \(\large x\ne 0\)

Answer 16

what does that mean? ;)

Answer 17

it just means, the expression is okay for all values of \(x\), except 0

Answer 18

well I get what it's saying but I'm not sure how the 6x^2 would be affected

Answer 19

think of a physical situtation where the given expression models something like the cost of drinking water :


\(\large f(x) = 6x^2\)

Answer 20

where, x = number of liters of water consumed

Answer 21

oh yeah that makes sense ;) so even if x is not equal to 0. is the answer that I got even going to change even with the restriction?

Answer 22

we can add the restriction :
\[\large f(x) = 6x^2, ~~x\ne 0\]
the function gives you cost for all values of x, except 0.
because there may be a fixed water charge even if u haven't used any drinking water ?

Answer 23

thats one of the purposes of restrictions - they tell you for what values the function is NOT defined.

Answer 24

I see..

Answer 25

the cost function will not give you the cost for 0 liters of water usage,
if you plugin x = 0, what would u get ?

Answer 26

0

Answer 27

you get \(\large f(0) = 6(0)^2 = 0\)
however we need to pay a fixed charge even if we haven't used any water, right ?

so we put the restriction on the function and say, the function is defined for all x except 0 : \(x \ne 0\)

Answer 28

this becomes more clear when u do piece wise functions :)

Answer 29

so the answer wouldn't change? it would still be 6x^2

Answer 30

answer is \(\large 6x^2 , ~~~x\ne 0\)

Answer 31

so the last option? ;)))

Answer 32

Yes, because the restriction is part of the question and applies to all answers.