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anonymous
 one year ago
27^4/3
How do I solve this?
anonymous
 one year ago
27^4/3 How do I solve this?

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Nnesha
 one year ago
Best ResponseYou've already chosen the best response.3\[\huge\rm x^{m} = \frac{ 1 }{ x^m }\] if there is a negative exponent then you should flip the fraction

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@Nnesha okay what do I do after that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[27^{\frac{ 4 }{ 3 }} = \frac{ 1 }{ 27^\frac{ 4 }{ 3 } } = \frac{ 1 }{ \left( 27^\frac{ 1 }{ 3 } \right)^4 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And\[x^\frac{ 1 }{ 3 } = \sqrt[3]{x}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm a bit confused with that second equation. How/when would I use that?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, any time you have a fractional exponent, the denominator of the fraction is the root that is required. In other words,\[x^\frac{ n }{ m } = \sqrt[m]{x^n}\]And you have a fractional exponent in your question.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Put simply, you can simplify \(27^\frac{1}{3}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So does 4/3 get plugged into that or does 1/3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I already converted my equation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry. I don't understand. Are you able to simplify\[\frac{ 1 }{ \left( 27^\frac{ 1 }{ 3 } \right)^4 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't think so, but I'm asking if I use the exponent 4/3 or the exponent 1/3 to plug into that rational expression

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0This problem involves two exponent rules. 1. a negative exponent 2. a fractional exponent Here are the rules you need: Negative exponent: \(\Large a ^{n} = \dfrac{1}{a^n} \) Fractional exponent: \(\Large a^{\frac{m}{n}} = \sqrt[n] {a^m} = \left( \sqrt[n] a \right)^m \)

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439436483720:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439436579962:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Let's use the negative exponent rule first. dw:1439436586340:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439436666466:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0We break the fractional exponent into two parts and use the "power to a power" rule\[27^\frac{ 4 }{ 3 } = 27^{\frac{ 1 }{ 3 }\times4} = \left( 27^\frac{ 1 }{ 3 } \right)^4\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I understand that so far but which exponent do I use? The already converted exponent?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0The negative exponent is already taken care of. Now let's take care of the fractional exponent: dw:1439436644180:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Order of operations. Calculate what 27^(1/3) is and raise that number to the 4th power.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0The fractional exponent has been taken care of, and now you have a cubic root and an exponent. Take the cubic root of 27. Then raise it to the 4th power.

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0@ospreytriple the order will not matter you will get the same result the only operation is really multiplication

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm sorry...I'm on the app so the links or equations y'all are trying to show me aren't working. I can see the computerized version...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@triciaal , I hope you'll agree it's a lot easier to take the cube of 27 and raise that result to the 4th power than it is to raise 27 to the 4th power and then take the cube root. Technically, you are correct of course, but there are practical concerns to consider.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes. 3^4. The cube root of 27 is 3.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439437072181:dw

triciaal
 one year ago
Best ResponseYou've already chosen the best response.0of course I agree that is fastest for this problem but I was addressing what you said about the order of operations

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I was following the order of operations as I wrote it (with brackets).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@achara.the.blasian, you're almost there. What is 3^4?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, don't forget, it's 1/81.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ohhhhh okay. So what do I do with that?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439437425872:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That's your answer. The question requires you to simplify the given expression. And you have. Good job.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much everyone
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