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SAT II Math I : Simplifying Expressions

Study concepts, example questions & explanations for SAT II Math I

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All SAT II Math I Resources

6 Diagnostic Tests 113 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #21 : Simplifying Expressions

Simplify the expression $\frac{x^5(3x^2y^3)}{x^4y^2z}$

Possible Answers:

Already in simplest form

3x^3y

$\frac{3x^6y}{z}$

$\frac{3x^3y}{z}$

$\frac{3x^3}{yz}$

Correct answer:

$\frac{3x^3y}{z}$

Explanation:

$\frac{x^5(3x^2y^3)}{x^4y^2z}$

Simplify the numerator by multiplying in the $\tiny x^5$ term

$\frac{3x^7y^3}{x^4y^2z}$

Cancel out like terms in the numerator and denominator.

$\frac{3x^3y}{z}$

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Example Question #22 : Simplifying Expressions

Simplify: $(x^2)\cdot (\frac{x^{-1}}{x})$

Possible Answers:

$\frac{1}{x}$

$\frac{1}{x^3}$

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

x^3

Correct answer:

Explanation:

Rewrite the denominator of the second fraction using a power.

$(\frac{x^{-1}}{x}) = (\frac{x^{-1}}{x^1})$

Using the subtraction rule of exponents, we can simplify this as one term.

$x^{-1-1} = x^{-2}$

The expression becomes:

$(x^2)\cdot (x^{-2})$

Apply the addition rule of exponents.

$x^{2+(-2)} = x^0 =1$

The answer is:

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Example Question #23 : Simplifying Expressions

$\frac{(x^7 - x^6)}{ (x - 1)} =$

Possible Answers:

x^6 - x^5

x^5

$\frac{1}{x-1}$

x^6

$\frac{x}{(x-1)}$

Correct answer:

x^6

Explanation:

Factor an x^6 in the numerator to get:

$\frac{(x^7 - x^6)}{ (x - 1)} =\frac{x^6(x-1)}{(x-1)}$

We can now cancel out (x-1) from the numerator and denominator leaving the answer.

x^6

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All SAT II Math I Resources

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SAT II Math I : Simplifying Expressions

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #21 : Simplifying Expressions

Example Question #22 : Simplifying Expressions

Example Question #23 : Simplifying Expressions

All SAT II Math I Resources

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