Question

Please help medal and fan!!!!!
I'm so confused how to do this type of problem, please explain!!!!

Answer 1

@misty1212 this one is different so idk :/

Answer 2

@BlossomCake @bohotness @Compassionate @InExileWeTrust @EclipsedStar

Answer 3

@misty1212

Answer 4

Somebody please help me!!!!

Answer 5

say something @plusky

Answer 6

so ik can give you a medal

Answer 7

don't just give them a medal

Answer 8

That is breaking the CoC ._. .-.

Answer 9

no its because he help me on my other question and i said i was going to give him a medal but i acedently closed it.

Answer 10

oh, u still can give medals in closed questions

Answer 11

Go to closed questions, or to your "asked questions" on your profile

Answer 12

@iGreen @animal_lover36 @thomaster @TheEdwardsFamily Can someone help me?

Answer 13

they want you to first learn how to "rewrite" radicals using exponents
Here is the rule:
\[ \sqrt[a]{b}= b^\frac{1}{a} \]

Answer 14

ok

Answer 15

try to match up your problem with the rule:
\[ \sqrt[4]{9} \]
which number matches with "a"
which number with "b"

Answer 16

9 is b, 4 is a

Answer 17

9 1/4

Answer 18

now use the other side to write it as
\[ 9^\frac{1}{4} \]
so far , so good

Answer 19

you should put in an ^ like this: 9^(1/4) so we know the 1/4 is an exponent

Answer 20

if you don't see a number in the "a" position, we *assume it is 2*

Answer 21

ok

Answer 22

so can you translate
\[ \sqrt{9} = \sqrt[2]{9}= ?\]

Answer 23

match
\[ \sqrt[2]{9} \] to the rule

Answer 24

9^(1/2)

Answer 25

yes.

that (for the moment) takes care of the top. But we will return to that later
now for the bottom
\[ \sqrt[4]{9^5} \]
we use the same rule, except "b" is not just 9, it is 9^5

Answer 26

ok but then how does the 1/4 work with the 9^5?

Answer 27

you put parens around 9^5 and think of it as "one thing"
then write the exponent 1/4 in the upper right side in little numbers

Answer 28

ok so like (9^5)^1/4?

Answer 29

yes, exactly

Answer 30

ok

Answer 31

but (of course) there are ways to "simplify" that.
it turns out, if you have
\[ \left(a^b\right)^c \]
you can rewrite it as
\[ \left(a^b\right)^c = a^{bc}\]

Answer 32

oh, ok

Answer 33

try to match up
\[ \left(9^5\right)^\frac{1}{4} \]
with the rule

Answer 34

so 9^5 1/4?

Answer 35

yes if you mean 5 times 1/4
for the exponent.

but you can write
\[ 5 \cdot \frac{1}{4} = \frac{5}{4} \]
if you remember how to multiply a number times a fraction

Answer 36

in case you did not know, in algebra (i.e. when we write rules using letters)
the bc in the rule is short for b*c (b times c)

Answer 37

ohh ok
yeah i know about the bc and b*c

Answer 38

now let's write what we have so far
\[ \frac{ 9^\frac{1}{4}9^\frac{1}{2} }{9^\frac{5}{4}} \]

Answer 39

ok

Answer 40

when you multiply numbers with the *same base* (and here we have 9 as the base)
we can add the exponents.
for the top we can add 1/4 + 1/2
can you do that ?

Answer 41

yeah
3/4

Answer 42

that means the top can be rewritten
\[ 9^\frac{1}{4}9^\frac{1}{2} = 9^\frac{3}{4} \]

Answer 43

ok

Answer 44

Then it will be 9 3/4 over 9 5/4

Answer 45

yes, good.
you have
\[ \frac{ 9^\frac{3}{4} }{9^\frac{5}{4}} \]
the other rule, is if you divide (and you have the same base), subtract the "bottom" exponent from the top exponent

Answer 46

9 8/4
then simplified to 9^2

Answer 47

you added?? (which you would do if the problem was \( 9^\frac{3}{4} 9^\frac{5}{4} \) )
remember: subtract if you are dividing

Answer 48

if you divide (and you have the same base), subtract the "bottom" exponent from the top exponent

Answer 49

oh, sorry

Answer 50

So -2/4
9^-1/2?

Answer 51

yes. You had to use every trick in the book to do this problem

Answer 52

ok. Thanks for helping!! I finally understand

Answer 53

it might help you to remember these rules if you remember a simple problem
for example \(3^2 \) means 3*3
if you multply \( 3^2 \cdot 3^1\) you know the answer is 3*3*3, which is \(3^3\)
and that might help you to remember to add the exponents.

or
\[ \frac{3\cdot 3}{3} = 3 \]
or using exponents
\[ \frac{3^2}{3^1}= 3^1 \]
notice you subtract exponents

Answer 54

ok