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

## Example Questions

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### Example Question #171 : Algebra

What is  in exponential notation?

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

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 .

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 .

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

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 .

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

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 .

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 .

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

?

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.