Question

((This is probably a really easy problem but i need help pls))

What is the simplest form of 16^3/4?

a.8
b.12
c.24
d.64

Answer 1

16^(3/4)

16^(3*1/4)

16^(1/4*3)

[ 16^(1/4) ] ^3

[ 4th root of 16 ] ^3

[ 2 ] ^3

8


Hopefully all that makes sense. If not, then let me know

Answer 2

I'm using the ideas that

x^(y*z) = (x^y)^z

and

x^(1/n) = nth root of x

Answer 3

woah okay, take that a little slower omg

Answer 4

sorry about that

Answer 5

which step isn't making sense?

Answer 6

16^(3/4) is equal to \[\sqrt[4]{16}^{3}\]
because \[x ^{\frac{ n }{ m }} = (\sqrt[m]{x})^{n}\]

4th root of 16 is 2 because 2x2x2x2 = 16.

So you end up with\[2^{3} = 8 \]

Answer 7

what are you doing to simplify 3/4

Answer 8

I turned 3/4 into 3*1/4

I wanted to pull out that 3 so to speak so I can be left with 1/4

then I'd use the rule that TripleC just posted

Answer 9

@jim_thompson5910 Who needs to pull it out when you can do it in one big bang?

Answer 10

that's true, you have a much simpler/shorter way to do it

Answer 11

ok ok, so if it was another one like idk 24 ^5/6, you would make it, ^6 sqrt 24 ^5??

Answer 12

\[(\sqrt[6]{24})^{5}\]

Answer 13

That just needs bunging into a calculator or left alone as an evaluated form.

Answer 14

So yeah you were right xD

Answer 15

alright, this makes more sense haha

Answer 16

@jim_thompson5910 can you help with another one really quick??

Answer 17

sure, what do you need

Answer 18

solution for x= sqrt -x+6

Answer 19

so the equation is

\[\large x = \sqrt{-x+6}\]

right?

Answer 20

yes (:

Answer 21

ok great

Answer 22

first you square both sides to get rid of that square root, then you get everything to one side, then factor like so

\[\large x = \sqrt{-x+6}\]

\[\large x^2 = (\sqrt{-x+6})^2\]

\[\large x^2 = -x+6\]

\[\large x^2 + x-6=0\]

\[\large (x+3)(x-2)=0\]

I'll let you finish. Make sure you check all of your possible answers.

Answer 23

would you distribute, so it would be like x^2-6??

Answer 24

no you use the zero product property

so

(x+3)(x-2)=0

turns into

x+3 = 0 or x-2 = 0

then you solve each for x to get

x = -3 or x = 2

I'll let you check these answers

Answer 25

okay, so would the zero property change whether its positive or negative

Answer 26

the zero product property is the idea that if

A*B = 0

then

A = 0 or B = 0

Answer 27

okay because for the problem, it was 3 and -2, but the answer was -3 and 2

Answer 28

well that's because when you solve x+3 = 0, you get x = -3

see how that works out?

Answer 29

oh okay i got it(:

Answer 30

I'm glad you do

Answer 31

thank you so much ((:

Answer 32

you're welcome