7. Use the quotient rule to simplify the following expression. Assume that x>0.

The answer after simplifying the expression is 8x .
Quotient rule simply states that as long as the base is the same, we can just divide two powers by subtracting the exponents.
This is a shortcut to simplify exponents.
The given expression is
[tex]\rm\dfrac{\sqrt{192 x^{3}}}{\sqrt{3x}}[/tex]
now simplifying
as they both have square root so can be written as
[tex]\rm\sqrt{\dfrac{{192 x^{3}}}{{3x}}}[/tex]
now we can divide the x³ and x to get x² and 192 can be divide by 3 to get 64
[tex]\rm\sqrt{64x^{2}}[/tex]
now this can written as 8x.
Therefore after simplifying the equation we get 8x .
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