Question

Simplify this exponent fraction

Answer 1

@DanJS @Jhannybean

Answer 2

hi

Answer 3

yo.

Answer 4

multiply the denomiators power to the power terms

Answer 5

2x^-6 and y^14?

Answer 6

Right, just had to include the 2 in there also
\[\frac{ 3x ^{-4}*y^5 }{ 2^{-2}* x ^{-6}*y ^{14} }\]

Answer 7

now, move any negative exponents to the oposite side of the fraction

Answer 8

recalling:
\[x^a *x^b = x ^{a+b}\]

Answer 9

so divide the terms basically?

Answer 10

so move the x^-6 to the top and add it to the x^-4 power

Answer 11

you do not want negative exponents in your final simplification

Answer 12

add to the negative 4?

Answer 13

see what happened there

Answer 14

\[\frac{ 2^2*3*x ^{-4+6} }{ y ^{14-5} }\]

Answer 15

can you explain that step again

Answer 16

The 2^(-2) in the bottom was moved to the top, by simply switching the sign on the exponent, and the x and y terms were combined based on which way would leave a positive exponent.

The rules used are:
\[\frac{ 1 }{ a ^{-b} } = \frac{ a^b }{ 1 }\]
\[[a^b]^c = a ^{b * c}\]
\[a^b + a^c =a ^{b + c} \]

Answer 17

oops, the last one is
\[a^b*a^c = a ^{b+c}\]

Answer 18

So the final answer is...?

Answer 19

Wait, so for the x on the numerator and denominator im allowed to switch the signs for both, then add?

Answer 20

so instead of 4+(-6) i can do -4+6?

Answer 21

yeah, here...

Answer 22

\[\frac{ x ^{-4} }{ x ^{-6} } = \frac{ x ^{-4 + 6} }{ 1 } = \frac{ x ^{2} }{ 1 }\]

Answer 23

Same with the y's, you have

y^5 / y^14

Move the 5 down to the bottom, becomes a -5, y to the 14 - 5

Answer 24

lol. didn't see that the x was a negative 4...had it as a positive ^4 on my paper the whole time..

Answer 25

ahhh, you get the rules though?

Answer 26

so instead of 4+(-6) i can do -4+6?
it can be like this ??????

Answer 27

for the x term yeah

Answer 28

(x^a)*(x^b) = x^(a+b)

Answer 29

wait for the y's of y^5/y^14 what signs do i change to make the exponent positive?

Answer 30

the numerator is x to the -4
the denominator is x to the -6

move the denominator to the top and it becomes a +6

x^(-4)* x^(6) = = x^(-4+6)

Answer 31

you move the y^5 to the bottom, and remember when you do that , you have to change the sign on the exponent

Answer 32

it becomes y^14-5)

Answer 33

wait how that's become 14-5
y^14 is a denominator so 14 should move at the top suppose to be 5-14

Answer 34

he switched it so you can move to bottom to..i guess

Answer 35

@DanJS

since i put y^14-5, the y is for the denominator now, right?

Answer 36

then you should get negative exponent then you have to back to den.