SSAT Upper Level Math : How to find the properties of an exponent

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

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Example Question #171 : Algebra

What is  in exponential notation? 

Possible Answers:

Correct answer:

Explanation:

Exponential notation includes a base number and an exponent. The base number is the number that is being multiplied and the exponent is how many times the base number is being multiplied to itself.

In this case,  is our base number and it's being multiplied to itself  times, so that is our exponent.  

Example Question #122 : Properties Of Exponents

Possible Answers:

Correct answer:

Explanation:

Apply the Power of a Product Principle:

Setting   and , keeping in mind that an odd power of a negative number is negative:

Example Question #123 : Properties Of Exponents

 and 

Evaluate .

Possible Answers:

Correct answer:

Explanation:

 and  is positive, so 

.

The greatest perfect square factor of 12 is 4, so the radical can be simplified:

, and  is positive, so 

By the Power of a Power Property, 

It is easiest to note that this can be broken up by the Product of Powers Principle, and evaluated by substitution:

The greatest perfect square factor of 60 is 4, so the radical can be simplified:

Example Question #124 : Properties Of Exponents

 and  are both positive.

Evaluate .

Possible Answers:

Correct answer:

Explanation:

By the difference of squares pattern:

By the Power of a Power Principle,

Substituting 75 and 3 for  and , respectively:

Example Question #125 : Properties Of Exponents

Possible Answers:

Correct answer:

Explanation:

By the Power of a Power Principle, 

Substituting  for , keeping in mind that an even power of any number must be positive:

Example Question #126 : Properties Of Exponents

 and 

Evaluate .

Possible Answers:

Correct answer:

Explanation:

By the perfect square trinomial pattern,

 and .

Also, by the Power of a Power Principle, 

so, since  and  are both positive, 

.

Therefore, 

 

Example Question #127 : Properties Of Exponents

Possible Answers:

Correct answer:

Explanation:

By the Power of a Power Principle, 

Therefore, we substitute, keeping in mind that an odd power of a negative number is also negative:

Example Question #128 : Properties Of Exponents

 and 

Evaluate .

Possible Answers:

Correct answer:

Explanation:

By the perfect square trinomial pattern,

 and .

Also, by the Power of a Power Principle, 

so, since  and  are both positive,

.

Therefore, 

And, substituting:

Example Question #129 : Properties Of Exponents

Evaluate the expression .

Possible Answers:

Correct answer:

Explanation:

Multiply out the expression by using multiple distributions and collecting like terms:

Since  by the Power of a Power Principle,

.

However,  is positive, so  is as well, so we choose .

Similarly, 

.

However, since  is negative, as an odd power of a negative number,  is as well, so we choose .

Therefore, substituting:

 

Example Question #121 : How To Find The Properties Of An Exponent

 and  are both positive integers; A is odd. What can you say about the number 

 ?

Possible Answers:

 is even if  is odd, and odd if  is even.

 is even if  is odd, and can be odd or even if  is even.

 is odd if  is odd, and can be odd or even if  is even.

 is odd if  is odd, and even if  is even.

 is even if  is even, and can be odd or even if  is odd.

Correct answer:

 is odd if  is odd, and even if  is even.

Explanation:

If  is odd, then , the sum of three odd integers, is odd; an odd number taken to any positive integer power is odd.

If  is even, then , the sum of two odd integers and an even integer, is even; an even number taken to any positive integer power is even. 

Therefore,  always assumes the same odd/even parity as .

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