Rewrite using only positive exponent: (2y^3*3xy^3)/ (3x^2*y^4) (2x^3 *z^2)^3 / (x^3*y^4 *z^2 * x^-4*z^3)

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

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Let E = (2y^3*3xy^3)/ (3x^2*y^4) (2x^3 *z^2)^3 / (x^3*y^4 *z^2 * x^-4*z^3)

==> E = (x^3*z^2*x^-4 *z^3)(2y^3*3xy^3)/(3x^2*y^4(2x^3*z^2)^3

==> E = (x^3*z^2*x^-4*z^3)(2y^3*3xy^3)/(3x^2*y^4)(8x^9*z^6)

We will use the exponent properties to simplify:

we know that: a^b/ a^c = a^(b-c)

also, we know that: a^b * a^c = a^(b+c)

==> E = 6x^0 * y^6*z^5)/(24x^11*y^4*z^5)

           = y^(6-2) *z^5-5)/ 4x^11

           = y^4/ 4x^11

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kjcdb8er | Teacher | (Level 1) Associate Educator

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Rewrite:

(2y^3*3xy^3)/ (3x^2*y^4) (2x^3 *z^2)^3 / (x^3*y^4 *z^2 * x^-4*z^3)

 

= (2y^3*3xy^3)/ (3x^2*y^4) (2x^3 *z^2)^3 * 1/(x^3*y^4 *z^2 * x^-4*z^3)

 

= 16 x^8 y^2 z^6 * 1/(x^3*y^4 *z^2 * x^-4*z^3)


=16 x^8 y^2 z^6 *x/(y^4 z^5)


= (16 x^9 z)/y^2

 

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