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.

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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.

Mathematics
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  • phi
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?
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Other answers:

i guess
  • phi
5/4 means divide 4 into 5, plus a remainder that you "put over" 4
if you divide 4 into 5 it's 0.8
  • phi
that is 4/5 = 0.8 in other words you did 5 divided into 4
either I'm stupid or i just don't get what you're saying
  • phi
Can you post a copy of the question?
yes hold on
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What he's trying to say is you need to do the problem 5 divided by 4 as a starter
  • phi
oh, that is different from what I thought 5/4 is an exponent
Oh same here :/
5 divided by 4 is 1.25
Ok so basically this problem is asking what is 16 to the power of 1.25 right @phi
  • phi
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"
Right
  • phi
to find the 4th root (which is generally hard to do, but possible here) we should factor 16 into 2*2*2*2 = \(2^4\)
  • phi
do you see that 2 times itself 4 times is 16 ?
81?
  • phi
so we write 16 as 2^4 \[ \left( 16^\frac{1}{4}\right)^5 = \left( (2^4)^\frac{1}{4}\right)^5\]
  • phi
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 ?
I'm stupid and lost
do 2x2x2x2
right?
  • phi
the rule \( (a^b)^c = a^{bc} \) means if you have an exponent b and another exponent c , we can multiply them
  • phi
you "match the pattern" \[ (a^b)^c = a^{bc} \\ (2^4)^\frac{1}{4} \]
  • phi
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)
  • phi
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 ?
  • phi
the idea is we can rewrite (2^4)^(1/4) using that rule \[ 2^{4 \cdot \frac{1}{4} }\]
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
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
  • phi
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 ?
1/4
  • phi
\[ \frac{1}{4} \cdot 5 = ?\] (as an improper fraction)
sorry 1.25
  • phi
ok, but not as a decimal. what about as a fraction ?
no i dont i just know what it is as a decimal because my phone told me
  • phi
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 \[ \frac{1}{4} \cdot 5=?\]
5/4
  • phi
yes. the reason we want to know that is we can say \[ \frac{5}{4}= \frac{1}{4} \cdot 5 \] and vice versa
  • phi
and there is a rule that let's us write \[ 16^\frac{5}{4} = (16^\frac{1}{4})^5 \]
so now i know where you got 1/4
  • phi
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
  • phi
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) )
  • phi
do you know how to use the "short-cut" way using exponents to write 2*2*2*2 ? in other words that is 2^?
  • phi
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 ?
the answer 17 1/4
  • phi
do you know \(2^1 = 2 \) and \( 2^2 = 2\cdot 2\) and \(2^3 = 2\cdot 2\cdot 2\) ?
yes
  • phi
ok, so how do we write \[ 2\cdot 2\cdot 2\cdot 2= 2^? \]
2 to the 4 power
  • phi
ok, so we know 16= 2*2*2*2 and that is 2^4
  • phi
\[ (16^\frac{1}{4})^5 \\ ((2^4)^\frac{1}{4})^5 \]
  • phi
now let's use the rule on \[ (2^4)^\frac{1}{4} \] remember we can multiply the exponents ?
so I multiply 2^4 by 1/4?
  • phi
you multiply the exponents , so just 4*1/4 and that is the new exponent
1
  • phi
that means \[ (2^4)^\frac{1}{4} = 2^1 \]
  • phi
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
(2^1)5 is 10
  • phi
no, not 10 it is (2^1)^5 i.e. \( (2^1)^5\) multiply the exponents (that means 1 and 5)
5
  • phi
yes, and that means 5 is the new exponent. so (2^1)^5 = 2^5 ok ?
okay i get that
  • phi
they may want you to multiply that out for the final answer what is 2 times itself 5 times ?
32
  • phi
yes, that is the answer
thank you so much for helping me and last question are you a math teacher?
  • phi
no
you need to be

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