Question

Which expression is equivalent to startfraction 10 x superscript 6 baseline y superscript 12 baseline over negative 5 x superscript negative 2 baseline y superscript negative 6 baseline endfraction? assume x not-equals 0, y not-equals 0.

Answer 1

$3/ 5x^6*y^6$ is the solution f the expression $(-9x^-1*y^-9) / (-15x^5*y^-3)$

Given expression:

(-9x^-1*y^-9) / (-15x^5*y^-3)

As we know, any number with negative power can be written in inverse form with positive power.

$x^-a = 1/x^a$

Two number having same base their powers are added:

$x^a + x^b = x^a+b$

$= > (-9x^-1*y^-9) / (-15x^5*y^-3)= (-3x^-1*y^-9) / (-5x^5*y^-3)\\=3/(5x^6 y^6)$

Hence the solution would be $3 (5x^6 y^6)$.

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