TheYankee
  • TheYankee
Higher roots with exponents?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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TheYankee
  • TheYankee
How do I simplify?
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Nnesha
  • Nnesha
factor x^{16} remember exponent rules \[\huge\rm x^m \times x^n = x^{m+n}\]
Nnesha
  • Nnesha
so you can write x^5 times x^5 times x^5 times x which is equal to ??

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Nnesha
  • Nnesha
\[\huge\rm x^5 \times x^5 \times x^5 \times x= x^?\]
Nnesha
  • Nnesha
when we multiply same bases we should add their exponents :-) exponent rules \[\huge\rm x^m \times x^n = x^{m+n}\]
TheYankee
  • TheYankee
So, would it look like this?
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Nnesha
  • Nnesha
\[\huge\rm x^5 \times x^5 \times x^5 \times x= x^?\] you didn't answer my question :(
TheYankee
  • TheYankee
Wouldn't it be x^16? (I have such a problem with these >.< )
Nnesha
  • Nnesha
yes right
Nnesha
  • Nnesha
now factor them under the 5th root \[\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times x }\] just like square can cancelz out with square same idea here &that's why we have to make a pair of five exponent so we cancel them with 5th root solve that
Nnesha
  • Nnesha
you can convert root to exponent \[\huge\rm \sqrt[n]{x^m}= x^\frac{ m }{ n }\]
TheYankee
  • TheYankee
Oh! Alright! I didn't know that! (Please excuse my ineptitude... I'm a history person, lol....)
TheYankee
  • TheYankee
Huh! Would it be X^4, then?
Nnesha
  • Nnesha
convert 5th root to exponent
TheYankee
  • TheYankee
When you convert to an exponent, Each 5th root would result in one, correct? Making it just X instead of x rasied to a power.
Nnesha
  • Nnesha
yes right but x is same as x to the one power x^1
TheYankee
  • TheYankee
True. So because each x factor would result in x^1, I'm thinking the end result would be X^4.
Nnesha
  • Nnesha
\[\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times x }\] \[\huge\rm x^\frac{5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 1 }{ 5 }\] so it should be like this
Nnesha
  • Nnesha
\[\huge\rm \sqrt[5]{x^5 \times x^5 \times x^5 \times\color{reD}{ x} }\] red x doesn't have power so you cannot cancel 5th root. it should stay under the 5th rot \[\huge\rm x^\frac{5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 5 }{ 5 } \times x^\frac{ 1 }{ 5 }\] so it should be like this
TheYankee
  • TheYankee
Omg! It makes sense now! Would it be x^3 5^(sqrt) x? (I'll model that answer in a second. Thanks for your patience ^^)
Nnesha
  • Nnesha
yes!
Nnesha
  • Nnesha
np :-)
TheYankee
  • TheYankee
To confirm, like this?
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Nnesha
  • Nnesha
yes

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