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. Negative StartFraction 3 p Superscript 8 Baseline Over 4 q cubed EndFraction Negative StartFraction 3 Over 4 p Superscript 16 Baseline q Superscript 9 Baseline EndFraction Negative StartFraction p Superscript 8 Baseline Over 5 q cubed EndFraction Negative StartFraction 1 Over 5 p Superscript 16 Baseline q Superscript 9 Baseline EndFraction

Answer 1

Answer:

$- \frac{3}{4} \times  \frac{p^{8} }{q^{3} }$

Step-by-step explanation:

We have to find the quotient of the following division, $\frac{15p^{-4}q^{-6} }{- 20p^{-12} q^{-3}}$.

Now, $\frac{15p^{-4}q^{-6} }{- 20p^{-12} q^{-3}}$

= $- \frac{3}{4} p^{[- 4 - (- 12)]} q^{[-6 - (- 3)]}$ {Since all the terms in the expression are in product form, so we can treat them separately}

{Since we know the property of exponent as $\frac{a^{b} }{a^{c} } = a^{(b - c)}$}

= $- \frac{3}{4} p^{8} q^{-3}$

= $- \frac{3}{4} \times  \frac{p^{8} }{q^{3} }$ (Answer)

{Since we know, $a^{-b} = \frac{1}{a^{b} }$}

Answer 2

can be simplified to

$-\frac{3p^8}{4q^3}$

Hopes this helps

if not then I'm sorrr