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. \[x ^{\frac{ 1 }{ 3 }}\times x ^{\frac{ 1 }{ 3 }}\times x ^{\frac{ 1 }{ 3 }}\]

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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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@Nnesha hey you think you can help me real quick please?
first one is \[\huge\rm \sqrt[4]{x^3}\] ?
Yeah

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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
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
so let's do D first \[\huge\rm x^\frac{ 1 }{ 3} \times x^\frac{ 1 }{ 3 } \times x^\frac{ 1 }{ 3 }\]
for the first one it would be changed to |dw:1442352168592:dw|
yes right!
what about B ?
would it be |dw:1442352301079:dw|
perfecT!
can you try c ?
first rewrite sqrt{x^5} in exponent form
is it \[\huge\rm \sqrt[10]{x^5}\] ?
yeah
ok
would C. be |dw:1442352798917:dw|
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 = ?
right* not write
wouldn't it be 11/10
hmm no there is denominator so we should find common denomiantor
|dw:1442353149290:dw| 4+2 = 6 so 5/10+6/1
|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
no common denominator is 10 so that would stay the same |dw:1442353470101:dw| like this
let me know if you didn't understand that :=)
would we simplify it or that would be the end
simplify that
65/10
reduce the fraction
13/2
13/2
yes right so x^{13}/2 \[\huge\rm x^\frac{ 1 }{ 3} \times x^\frac{ 1 }{ 3 } \times x^\frac{ 1 }{ 3 }\]
what about D ??^
would it be x^1
yes right
so the two equivalent ones are D. and B.
yes right
thank you again so much
yw :=)

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