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What is the quotient StartFraction negative 8 a Superscript 8 Baseline b Superscript negative 2 Baseline Over 10 a Superscript negative 4 Baseline b Superscript negative 10 Baseline EndFraction in simplified form? Assume a not-equals 0, b not-equals 0.

Negative StartFraction 4 a Superscript 12 Baseline b Superscript 8 Baseline Over 5 EndFraction
Negative StartFraction 4 a Superscript 32 Baseline b Superscript 5 Baseline Over 5 EndFraction
StartFraction a Superscript 12 Baseline b Superscript 8 Baseline Over 80 EndFraction
StartFraction a Superscript 32 Baseline b Superscript 5 Baseline Over 80 EndFraction

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Answer:

A. Negative StartFraction 4 a Superscript 12 Baseline b Superscript 8 Baseline Over 5 EndFraction or -4a^12b^8/5

Step-by-step explanation:

Edg2020 - Just took test. :)

abidemiokin

The quotient of the given expression is [tex]-\frac{4}{5}a^{12}b^8[/tex]

Given the function:

  • [tex]\frac{-8a^8b^{-2}}{10^{-4}b^{-10}}[/tex]

Using the law of indices as shown:

  • [tex]a^m \times a^n = a^{m+n}\\\frac{a^m}{a^n} =a^{m-n}[/tex]

Applying this to the given functions:

[tex]=\frac{-8a^8b^{-2}}{10a^{-4}b^{-10}}\\=\frac{-8}{10} a^{8-(-4)}b^{-2-(-10)}\\=\frac{-4}{5} a^{8+4}b^{-2+10}\\=-\frac{4}{5}a^{12}b^8[/tex]

Hence the quotient of the given expression is [tex]-\frac{4}{5}a^{12}b^8[/tex]

Learn more on indices here: https://brainly.com/question/14484141

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