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All SAT Mathematics Resources

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Flashcards: Identifying Properties of Roots & Exponents

$\frac{(x^{4}y^{3})^{-2}}{(x^{3}y^{2})^{-4}}$

$x^{3}y^{3}$

$x^{4}y^{2}$

$x^{2}y^{2}$

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Flashcards: Identifying Properties of Roots & Exponents

$\frac{(x^{4}y^{3})^{-2}}{(x^{3}y^{2})^{-4}}$

Your answer:

$x^{3}y^{3}$

Your answer:

$x^{2}y^{2}$

Correct answer:

$x^{4}y^{2}$

Explanation:

Whenever you exponential expressions in both the numerator and denominator of a fraction, your first inclination might be to quickly simplify the expressions by canceling terms out in the numerator and denominator.

However, remember to follow the order of operations: you must simplify the numerator and denominator separately to revolve the exponents raised to exponents problem before you can look to cancel terms in the numerator and denominator.

If you consider the numerator, $(x^{4}y^{3})^{-2}$ , you should recognize that, because there is no addition or subtraction within the parentheses, that you can simplify this expression by multiplying each exponent within the parentheses by to get:

$x^{-8}y^{-6}$ .

Similarly, you can simplify the denominator, $(x^{3}y^{2})^{-2}$ by multiplying each exponent within the parentheses by to get:

$x^{-12}y^{-8}$ .

You can then recombine the numerator and denominator to get $\frac{x^{-8}y^{-6}}{x^{-12}y^{-8}}$ . Notice that you now have simple division. Remember that anytime you want to combine two exponential expressions with a common base that are being divided, you simply need to subtract the exponents. If you do, you get:

$x^{-8-(-12)}y^{-6-(-8)}$ , which simplifies to $x^{4}y^{2}$ .

Remember that if you forgot any of the rules, such as how to combine exponents with common bases that are being divided or whether you add or multiply when raising a power to a power, that you can always remind yourself how the rules work by testing small numbers.

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Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

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All SAT Mathematics Resources

Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

Flashcards: Identifying Properties of Roots & Exponents

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DMCA Complaint

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