How do you simplify $root5(x^3)/root7(x^4)$ ?

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Answer 1 · 2016-07-30T14:51:22

$" "x^(3/5)/x^(4/7) = x^(1/35) = root(35)(x) larr" 35th root"$

Write as: $(x^(3/5))/(x^(4/7)$

This is the same as: $x^(3/5-4/7)$

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Consider the $3/5-4/7$

Write as $(3/5xx1)-(4/7xx1)$

This is the same as: $(3/5xx7/7)-(4/7xx5/5)$

$=21/35-20/35 = (21-20)/35= 1/35$
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So $" "x^(3/5)/x^(4/7) = x^(1/35) = root(35)(x) larr" 35th root"$

Answer 2 · 2016-07-30T14:57:35

$x^(1/20) = root20(x)$

If both roots were the same we could have combined them into the root of a single fraction. But they are different.

Change to index form using : $" "rootq(x^p) = x^(p/q)$

$root5(x^3)/root7(x^4) = x^(3/5)/x^(4/7) " simplify using" x^m/x^n = x^(m-n)$

= $x^(3/5-4/7)$

= $x^((21-20)/35)$

= $x^(1/35) = root35(x)$

How do you simplify root5(x^3)/root7(x^4)root5(x^3)/root7(x^4)?