anonymous
  • anonymous
Which of the following expressions are equivalent? Justify your reasoning. Please help Thank you!! A. \[^{4\sqrt{x ^{3}}}\] B. \[\frac{ 1 }{ x ^{-1} }\] C.\[^{10}\sqrt{x ^{5}}\times x ^{4}\times x ^{2}\] D. \[x ^{\frac{ 1 }{ 3 }}\times x ^{\frac{ 1 }{ 3 }}\times x ^{\frac{ 1 }{ 3 }}\]
Mathematics
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@Nnesha hey you think you can help me real quick please?
Nnesha
  • Nnesha
first one is \[\huge\rm \sqrt[4]{x^3}\] ?
anonymous
  • anonymous
Yeah

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Nnesha
  • Nnesha
alright you should know some exponent rules for that question when we multiply same bases we should `add` exponents \[\huge\rm x^m \times x^n=x^{m+n}\] \[\huge\rm \sqrt[n]{x^m}=x^\frac{ m }{ n }\] you can convert root to an exponent form
Nnesha
  • Nnesha
exponent if there is a negative exponent `flip` the fraction \[\huge\rm x^{-m}=\frac{ 1 }{ x^m }\]when you flip the fraction sign of the exponent would change
Nnesha
  • Nnesha
so let's do D first \[\huge\rm x^\frac{ 1 }{ 3} \times x^\frac{ 1 }{ 3 } \times x^\frac{ 1 }{ 3 }\]
anonymous
  • anonymous
for the first one it would be changed to |dw:1442352168592:dw|
Nnesha
  • Nnesha
yes right!
Nnesha
  • Nnesha
what about B ?
anonymous
  • anonymous
would it be |dw:1442352301079:dw|
Nnesha
  • Nnesha
perfecT!
Nnesha
  • Nnesha
can you try c ?
Nnesha
  • Nnesha
first rewrite sqrt{x^5} in exponent form
Nnesha
  • Nnesha
is it \[\huge\rm \sqrt[10]{x^5}\] ?
anonymous
  • anonymous
yeah
Nnesha
  • Nnesha
ok
anonymous
  • anonymous
would C. be |dw:1442352798917:dw|
Nnesha
  • Nnesha
hmm not write \[\huge\rm x^{\frac{ 5 }{ 10 }+4+2}\] when we multiply same bases we should add their exponents so 5/10+4+2 = ?
Nnesha
  • Nnesha
right* not write
anonymous
  • anonymous
wouldn't it be 11/10
Nnesha
  • Nnesha
hmm no there is denominator so we should find common denomiantor
Nnesha
  • Nnesha
|dw:1442353149290:dw| 4+2 = 6 so 5/10+6/1
Nnesha
  • Nnesha
|dw:1442353207919:dw| it's like cross multiplication but don't forget the positive sign when we find common denominator we should multiply the `numerator` of 1st fraction by the denominator of 2nd fraction and multiply the numerator of *2nd *fraction by the denominator of first fraction
Nnesha
  • Nnesha
no common denominator is 10 so that would stay the same |dw:1442353470101:dw| like this
Nnesha
  • Nnesha
let me know if you didn't understand that :=)
anonymous
  • anonymous
would we simplify it or that would be the end
Nnesha
  • Nnesha
simplify that
anonymous
  • anonymous
65/10
Nnesha
  • Nnesha
reduce the fraction
anonymous
  • anonymous
13/2
anonymous
  • anonymous
13/2
Nnesha
  • Nnesha
yes right so x^{13}/2 \[\huge\rm x^\frac{ 1 }{ 3} \times x^\frac{ 1 }{ 3 } \times x^\frac{ 1 }{ 3 }\]
Nnesha
  • Nnesha
what about D ??^
anonymous
  • anonymous
would it be x^1
Nnesha
  • Nnesha
yes right
anonymous
  • anonymous
so the two equivalent ones are D. and B.
Nnesha
  • Nnesha
yes right
anonymous
  • anonymous
thank you again so much
Nnesha
  • Nnesha
yw :=)

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