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ISEE Upper Level Quantitative : Variables and Exponents

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Example Question #6 : How To Divide Exponential Variables

Simplify:

$\frac{10 x ^{-6} y ^{-4}}{20x ^{-8}y^{-2}}$

Possible Answers:

$\frac{1 }{2 x ^{2}y ^{2}}$

$\frac{2}{x ^{2}y ^{2} }$

$\frac{x ^{2}y ^{2} }{2 }$

$\frac{x ^{2} }{2y ^{2} }$

$\frac{y ^{2} }{2x ^{2} }$

Correct answer:

$\frac{x ^{2} }{2y ^{2} }$

Explanation:

Break the fraction up and apply the quotient of powers rule:

$\frac{10 x ^{-6} y ^{-4}}{20x ^{-8}y^{-2}}$

$= \frac{10 }{20} \cdot \frac{ x ^{-6} }{x ^{-8}} \cdot \frac{y ^{-4}}{y^{-2}}$

$= \frac{1 }{2} \cdot x ^{-6- (-8)} \cdot y ^{-4- (-2)}$

$= \frac{1 }{2} \cdot x ^{2} \cdot y ^{-2}$

$= \frac{1 }{2} \cdot x ^{2} \cdot \frac{1}{y ^{2}}$

$= \frac{x ^{2} }{2y ^{2} }$

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All ISEE Upper Level Quantitative Resources

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ISEE Upper Level Quantitative : Variables and Exponents

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

All ISEE Upper Level Quantitative Resources

Example Questions

Example Question #6 : How To Divide Exponential Variables

All ISEE Upper Level Quantitative Resources

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