Question

What is the quotient StartFraction 15 p Superscript negative 4 Baseline q Superscript negative 6 Baseline Over negative 20 p Superscript negative 12 Baseline q Superscript negative 3 Baseline EndFraction in simplified form? Assume p not-equals 0, q not-equals 0.

Answer 1

`-(3p^8)/(4q^3)`

Explanation:

`(15p^(-4)q^(-6))/(-20p^(-12)q^(-3))` can be broken down into three fractions, coefficients, powers of p, powers of q.

`-(15)/(20)\cdot(p^(-4))/(p^(-12))\cdot(q^(-6))/(q^(-3))`

Simplify the first fraction, then simplify the others by subtracting numerator exponents minus denominator exponents.

`-(3)/(4) p^(-4-(-12)) q^(-6-(-3)) =-(3)/(4) p^8 q^(-3) = \alpha -(3p^8)/(4q^3)`