Question

WILL FAN AND MEDAL

Answer 1

For the last one, add up all the fractions, x^a*x^b = x^(a+b)

Answer 2

the fourth root of x is the same as x^(1/4)

Answer 3

The last one you get x ^(16/4) = x^4

Answer 4

wait so this is al for Toms equation?

Answer 5

*all

Answer 6

Yeah tom, adds up to x^(16/4) or x^4

Answer 7

ohh ok thank you. do you know the other ones?

Answer 8

Lets see,

Answer 9

Tom
\[(\sqrt[3]{x})^{12} = x ^{\frac{ 12 }{ 3 }} = x ^{4}\]

Answer 10

That was Kevin, sorry

Answer 11

lol it's ok

Answer 12

Deb
\[\sqrt[4]{x^3 + x^5 + x^8 } = x ^{\frac{ 3 }{ 4 }} + x ^{\frac{ 5 }{ 4 }} + x ^{\frac{ 8 }{ 4 }}\]

Answer 13

3/4 + 5/4 + 8/4 = 16/4

\[x ^{\frac{ 16 }{ 4 }} = x ^{4}\]

Answer 14

Deb is good too

Answer 15

Joe is no good

Answer 16

oh so Deb is the correct one, alright

Answer 17

no, Deb, Kevin, and Tom are all correct

Answer 18

how do i do joe's? @DanJS

Answer 19

For joe...

Answer 20

oh wait sorry you already did it lol

Answer 21

no i didnt do joes yet

Answer 22

\[[x ^{5/4} * x ^{7/4} ] * x ^{-1/4}\]

Answer 23

When you have a exponent in the bottom, you can move it to the top by making it negative

Answer 24

Now distributing these, and adding their exponents gives,...
\[x ^{4/4} + x ^{6/4}\]

(5/4 - 1/4) = 4/4
(7/4 - 1/4) = 6/4

Answer 25

ooo i didn't know that

Answer 26

\[x ^{10/4} = x ^{5/2} \neq x^4\]

Answer 27

So joe is incorrect.

Answer 28

any part you dont understand?

Answer 29

ohhkay. thank you i appreciate it. i already fanned and gave you the medal lol

Answer 30

i think i understand

Answer 31

here is what you need to remember...

Answer 32

Just using

\[x^a * x^b = x ^{a + b}\]
\[\sqrt[a]{x} = x ^{1/a}\]
\[\frac{ 1 }{ x ^{a} } = x ^{-a}\]

Answer 33

oh so first i combine the base

Answer 34

The exponents

Answer 35

where does the b go for the second step?

Answer 36

like the first property, x to a power times x to another power, equals x to the powers added together

Answer 37

ohh so if im multiplying the base, i add the exponents?

Answer 38

No those are 3 separate properties of exponents.

Answer 39

yeah , the first property is if you have the same base multiplied together with exponents on them, you add the exponents

Answer 40

The second property is, if you have a root, it is the same thing as x raised to the 1/n power, where n is the root

Answer 41

like square root of x is the same as x raised to the 1/2 power
cubed root of x is the same as x raised to the 1/3 power

Answer 42

The third property, is if you have a base raised to a power in the denominator, you can move it to the top by making the power negative.

Answer 43

That is all you really have to remember.

Answer 44

The only other one, that was not in this problem is: a power raised to a power

\[(x ^{a })^{b} = x ^{a*b}\]

Answer 45

You multiply the powers in that case, not add them

Answer 46

ohh alright. gotchu

Answer 47

thank you for helping me understand :) @DanJS

Answer 48

no prob... just practice those 4 rules, and you will be able to do any problem with exponents