A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
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.
anonymous
 one year ago
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.

This Question is Closed

phi
 one year ago
Best ResponseYou've already chosen the best response.1simplest 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?

phi
 one year ago
Best ResponseYou've already chosen the best response.15/4 means divide 4 into 5, plus a remainder that you "put over" 4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if you divide 4 into 5 it's 0.8

phi
 one year ago
Best ResponseYou've already chosen the best response.1that is 4/5 = 0.8 in other words you did 5 divided into 4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0either I'm stupid or i just don't get what you're saying

phi
 one year ago
Best ResponseYou've already chosen the best response.1Can you post a copy of the question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What he's trying to say is you need to do the problem 5 divided by 4 as a starter

phi
 one year ago
Best ResponseYou've already chosen the best response.1oh, that is different from what I thought 5/4 is an exponent

anonymous
 one year ago
Best ResponseYou've already chosen the best response.05 divided by 4 is 1.25

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok so basically this problem is asking what is 16 to the power of 1.25 right @phi

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, 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"

phi
 one year ago
Best ResponseYou've already chosen the best response.1to 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
 one year ago
Best ResponseYou've already chosen the best response.1do you see that 2 times itself 4 times is 16 ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1so we write 16 as 2^4 \[ \left( 16^\frac{1}{4}\right)^5 = \left( (2^4)^\frac{1}{4}\right)^5\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1now use the rules of exponents we use this rule \[ (a^b)^c = a^{bc} \] on \[ (2^4)^\frac{1}{4} \] can you do that ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1the rule \( (a^b)^c = a^{bc} \) means if you have an exponent b and another exponent c , we can multiply them

phi
 one year ago
Best ResponseYou've already chosen the best response.1you "match the pattern" \[ (a^b)^c = a^{bc} \\ (2^4)^\frac{1}{4} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1we 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
 one year ago
Best ResponseYou've already chosen the best response.1look 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
 one year ago
Best ResponseYou've already chosen the best response.1the idea is we can rewrite (2^4)^(1/4) using that rule \[ 2^{4 \cdot \frac{1}{4} }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'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
 one year ago
Best ResponseYou've already chosen the best response.1the 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 ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ \frac{1}{4} \cdot 5 = ?\] (as an improper fraction)

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok, but not as a decimal. what about as a fraction ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no i dont i just know what it is as a decimal because my phone told me

phi
 one year ago
Best ResponseYou've already chosen the best response.1when 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 \[ \frac{1}{4} \cdot 5=?\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes. the reason we want to know that is we can say \[ \frac{5}{4}= \frac{1}{4} \cdot 5 \] and vice versa

phi
 one year ago
Best ResponseYou've already chosen the best response.1and there is a rule that let's us write \[ 16^\frac{5}{4} = (16^\frac{1}{4})^5 \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so now i know where you got 1/4

phi
 one year ago
Best ResponseYou've already chosen the best response.1if 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
 one year ago
Best ResponseYou've already chosen the best response.1so 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
 one year ago
Best ResponseYou've already chosen the best response.1do you know how to use the "shortcut" way using exponents to write 2*2*2*2 ? in other words that is 2^?

phi
 one year ago
Best ResponseYou've already chosen the best response.12*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 ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1do you know \(2^1 = 2 \) and \( 2^2 = 2\cdot 2\) and \(2^3 = 2\cdot 2\cdot 2\) ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok, so how do we write \[ 2\cdot 2\cdot 2\cdot 2= 2^? \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok, so we know 16= 2*2*2*2 and that is 2^4

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ (16^\frac{1}{4})^5 \\ ((2^4)^\frac{1}{4})^5 \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1now let's use the rule on \[ (2^4)^\frac{1}{4} \] remember we can multiply the exponents ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so I multiply 2^4 by 1/4?

phi
 one year ago
Best ResponseYou've already chosen the best response.1you multiply the exponents , so just 4*1/4 and that is the new exponent

phi
 one year ago
Best ResponseYou've already chosen the best response.1that means \[ (2^4)^\frac{1}{4} = 2^1 \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1so 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

phi
 one year ago
Best ResponseYou've already chosen the best response.1no, not 10 it is (2^1)^5 i.e. \( (2^1)^5\) multiply the exponents (that means 1 and 5)

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, and that means 5 is the new exponent. so (2^1)^5 = 2^5 ok ?

phi
 one year ago
Best ResponseYou've already chosen the best response.1they may want you to multiply that out for the final answer what is 2 times itself 5 times ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thank you so much for helping me and last question are you a math teacher?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.