PSAT Math : Exponents

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #2 : How To Factor A Common Factor Out Of Squares

Simplify the expression.

Possible Answers:

Correct answer:

Explanation:

Use the distributive property for radicals. 

Multiply all terms by .

Combine terms under radicals.

Look for perfect square factors under each radical.  has a perfect square of . The can be factored out.

Since both radicals are the same, we can add them.

Example Question #1 : Complex Numbers

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Multiply both numerator and denominator by :

Example Question #2 : Complex Numbers

Divide:

Possible Answers:

Correct answer:

Explanation:

Rewrite in fraction form, and multiply both numerator and denominator by :

 

Example Question #1 : Complex Numbers

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Multiply both numerator and denominator by :

Example Question #1 : Complex Numbers

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

 

Example Question #1 : How To Divide Complex Numbers

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

Example Question #2 : Complex Numbers

Simplify by rationalizing the denominator:

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is :

Example Question #7 : Complex Numbers

Define an operation  as follows:

For all complex numbers ,

.

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is . The above becomes:

Example Question #2 : How To Divide Complex Numbers

Define an operation  as follows:

For all complex numbers ,

.

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Example Question #9 : Complex Numbers

Define an operation  as follows:

For all complex numbers ,

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Multiply the numerator and the denominator by the complex conjugate of the denominator, which is . The above becomes:

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