# simplify the following & rewrite in equivalant form with positve exponets -18y^2y^4 / 6x^7y^2 must show all work

sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to change the variable `y^2`  from numerator in `x^2 ` because it is of no use to write the numerator in the given form if the bases y would be alike.

You need to isolate the constant terms, the terms containing powers of x and the terms containing powers of y such that:

`(-18/6) = -3`  constant terms

`(x^2)/(x^7)`  terms containing variable x

`(y^4)/(y^2) ` terms containing variable y

You need to use the property of division of powers that have like bases such that:

`(x^2)/(x^7) = x^(2-7) = x^(-5)`

Using the negative power property yields:

`x^(-5) = 1/(x^5)`

`(y^4)/(y^2) = y^(4-2) = y^2`

Multiplying the results of the three groups yields:

`(-18x^2y^4)/(6x^7y^2) = -3(y^2)/(x^5)`

Hence, simplifying the fraction to its lowest terms yields:

`(-18x^2y^4)/(6x^7y^2) =-3*y^2*x^(-5)`

justaguide | College Teacher | (Level 2) Distinguished Educator

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The expression `(-18x^2y^4)/(6x^7y^2)` has to be simplified.

`(-18x^2y^4)/(6x^7y^2)`

=> `-3*x^-5*y^2`

=> `(-3*y^2)/x^5`

The expression `(-18x^2y^4)/(6x^7y^2) = (-3*y^2)/x^5`

stargsd5 | Student, College Freshman | (Level 1) Valedictorian

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thank you for your help :)