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

7 Use The Quotient Rule To Simplify The Following Expression Assume That Xgt0 class=

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Quotient rule says we can divide 192 and 3 because they are both under the radical. This gives us the square root of 64.

We can also divide x^3 and x to get x^2.

The square root of 64x^2 is 8x

The answer after simplifying the expression is 8x .

What is Quotient Rule ?

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 .

To know more about Quotient Rule

https://brainly.com/question/15568137

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