Question

I really need help I don't have a math teacher so I'm trying learn this on my on so please someone help
What is 16 5/4 in simplest form?
There more questions but I'm putting the file down in the comments.

Answer 1

simplest form is a bit vague. But as a rule, if you see a fraction like
\[ \frac{5}{4}\] where the top is bigger than the bottom, that is an "improper fraction"
which means people would rather see it written as a mixed number
can you write 5/4 as a mixed number?

Answer 2

i guess

Answer 3

5/4 means divide 4 into 5, plus a remainder that you "put over" 4

Answer 4

if you divide 4 into 5 it's 0.8

Answer 5

that is 4/5 = 0.8
in other words you did 5 divided into 4

Answer 6

either I'm stupid or i just don't get what you're saying

Answer 7

Can you post a copy of the question?

Answer 8

yes hold on

Answer 9

What he's trying to say is you need to do the problem 5 divided by 4 as a starter

Answer 10

oh, that is different from what I thought
5/4 is an exponent

Answer 11

Oh same here :/

Answer 12

5 divided by 4 is 1.25

Answer 13

Ok so basically this problem is asking what is 16 to the power of 1.25 right @phi

Answer 14

yes, 5/4 = 1.25 but that is not the problem we have to solve here
the way we solve this is write the problem as
\[ \left( 16^\frac{1}{4}\right)^5 \]

the 1/4 power means the "fourth root"

Answer 15

Right

Answer 16

to find the 4th root (which is generally hard to do, but possible here)
we should factor 16 into
2*2*2*2 = \(2^4\)

Answer 17

do you see that 2 times itself 4 times is 16 ?

Answer 18

81?

Answer 19

so we write 16 as 2^4
\[ \left( 16^\frac{1}{4}\right)^5 = \left( (2^4)^\frac{1}{4}\right)^5\]

Answer 20

now use the rules of exponents
we use this rule
\[ (a^b)^c = a^{bc} \]
on
\[ (2^4)^\frac{1}{4} \]
can you do that ?

Answer 21

I'm stupid and lost

Answer 22

do 2x2x2x2

Answer 23

right?

Answer 24

the rule \( (a^b)^c = a^{bc} \)
means if you have an exponent b and another exponent c , we can multiply them

Answer 25

you "match the pattern"
\[ (a^b)^c = a^{bc} \\ (2^4)^\frac{1}{4} \]

Answer 26

we could do 2*2*2*2
but we don't want to (because if we use the exponent rule we will get a simpler answer)

Answer 27

look at these two things
\[ (a^b)^c = a^{bc} \\ (2^4)^\frac{1}{4} \]
do you see you can match a with 2, and 4 with b, and 1/4 with c ?

Answer 28

the idea is we can rewrite (2^4)^(1/4) using that rule
\[ 2^{4 \cdot \frac{1}{4} }\]

Answer 29

i see numbers that's makes no sense to why the hell letters are in a math problem and we are talking about 16 and a 5/4 so where in the world did a 2 and a 1 come form

Answer 30

I'm sorry that im getting mad and rude but i've been doing this all day and been have to learn this on my on

Answer 31

the letters are how to show a "rule"
we could use words, but it gets confusing.

anyway, we started with
\[ 16^\frac{5}{4} \]
we use a "rule" to write that a different way
\[ (16^\frac{1}{4})^5 \]

before going on, do you know what 1/4 * 5 is ?

Answer 32

1/4

Answer 33

\[ \frac{1}{4} \cdot 5 = ?\]
(as an improper fraction)

Answer 34

sorry 1.25

Answer 35

ok, but not as a decimal. what about as a fraction ?

Answer 36

no i dont i just know what it is as a decimal because my phone told me

Answer 37

when you multiply fractions, you multiply top times top and bottom times bottom
(if a number (like the 5) has no "bottom" , assume it is 1)
now try again
\[ \frac{1}{4} \cdot 5=?\]

Answer 38

5/4

Answer 39

yes. the reason we want to know that is
we can say
\[ \frac{5}{4}= \frac{1}{4} \cdot 5 \]
and vice versa

Answer 40

and there is a rule that let's us write
\[ 16^\frac{5}{4} = (16^\frac{1}{4})^5 \]

Answer 41

so now i know where you got 1/4

Answer 42

if you see
\[ (16^\frac{1}{4})^5\]
you should remember you are allowed to write it as
\[ 16^\frac{5}{4} \]
we need to be able to between these two different ways

Answer 43

so far we have
\[ (16^\frac{1}{4})^5\]

the next thing is to know we can write 16 as 2*2*2*2
(this is the hard part, knowing that. but now you do. (don't forget) )

Answer 44

do you know how to use the "short-cut" way using exponents to write
2*2*2*2 ?
in other words that is 2^?

Answer 45

2*2*2*2 is 2 to some power (some exponent)
do you know what little number we should put in the upper right of 2 so that it means 2*2*2*2 ?

Answer 46

the answer 17 1/4

Answer 47

do you know \(2^1 = 2 \)
and
\( 2^2 = 2\cdot 2\)
and
\(2^3 = 2\cdot 2\cdot 2\)
?

Answer 48

yes

Answer 49

ok, so how do we write
\[ 2\cdot 2\cdot 2\cdot 2= 2^? \]

Answer 50

2 to the 4 power

Answer 51

ok, so we know 16= 2*2*2*2 and that is 2^4

Answer 52

\[ (16^\frac{1}{4})^5 \\ ((2^4)^\frac{1}{4})^5
\]

Answer 53

now let's use the rule on
\[ (2^4)^\frac{1}{4} \]
remember we can multiply the exponents ?

Answer 54

so I multiply 2^4 by 1/4?

Answer 55

you multiply the exponents , so just 4*1/4 and that is the new exponent

Answer 56

1

Answer 57

that means \[ (2^4)^\frac{1}{4} = 2^1 \]

Answer 58

so now we have this
\[ (16^\frac{1}{4})^5 \\ ((2^4)^\frac{1}{4})^5 \\ (2^1)^5 \]
notice we can use the rule again to multiply the exponents on the last line

Answer 59

(2^1)5 is 10

Answer 60

no, not 10

it is (2^1)^5
i.e. \( (2^1)^5\)
multiply the exponents (that means 1 and 5)

Answer 61

5

Answer 62

yes, and that means 5 is the new exponent.
so (2^1)^5 = 2^5

ok ?

Answer 63

okay i get that

Answer 64

they may want you to multiply that out for the final answer
what is 2 times itself 5 times ?

Answer 65

32

Answer 66

yes, that is the answer

Answer 67

thank you so much for helping me and last question are you a math teacher?

Answer 68

no

Answer 69

you need to be