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What is the quotient [tex]\frac{15 p^{-4} q^{-6}}{-20 p^{-12} q^{-3}}[/tex] in simplified form? Assume [tex]p \neq 0, q \neq 0[/tex].

A. [tex]-\frac{3 p^8}{4 q^3}[/tex]

B. [tex]-\frac{3}{4 p^{16} q^9}[/tex]

C. [tex]-\frac{p^8}{5 q^3}[/tex]

D. [tex]-\frac{1}{5 p^{16} q^9}[/tex]

Sagot :

GinnyAnswer
To find the quotient \(\frac{15 p^{-4} q^{-6}}{-20 p^{-12} q^{-3}}\) in simplified form, we will simplify both the coefficients and the exponents.

1. Simplify the coefficient:
[tex]\[ \frac{15}{-20} = \frac{15}{-20} = -\frac{3}{4} \][/tex]

2. Simplify the exponents of \(p\):
[tex]\[ p^{-4} \div p^{-12} = p^{-4 - (-12)} = p^{-4 + 12} = p^{8} \][/tex]

3. Simplify the exponents of \(q\):
[tex]\[ q^{-6} \div q^{-3} = q^{-6 - (-3)} = q^{-6 + 3} = q^{-3} \][/tex]

Thus, combining these simplifications, the quotient can be written as:
[tex]\[ -\frac{3 p^8}{4 q^3} \][/tex]

So, the simplified form of [tex]\(\frac{15 p^{-4} q^{-6}}{-20 p^{-12} q^{-3}}\)[/tex] is [tex]\(\boxed{-\frac{3 p^8}{4 q^3}}\)[/tex].
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