PSAT Math : Exponents

Example Questions

Example Question #121 : Exponents

Explanation:

The key to this problem is understanding how exponents divide.  When two exponents have the same base, then the exponent on the bottom can simply be subtracted from the exponent on top.  I.e.:

Keeping this in mind, we simply break the problem down into prime factors, multiply out the exponents, and solve.

Example Question #1 : How To Divide Exponents

Simplify

None

Explanation:

Divide the coefficients and subtract the exponents.

Example Question #1 : How To Divide Exponents

Which of the following is equal to the expression , where

xyz ≠ 0?

z/(xy)

xyz

z

1/y

xy

1/y

Explanation:

(xy)4 can be rewritten as x4y4 and z0 = 1 because a number to the zero power equals 1.  After simplifying, you get 1/y.

Example Question #2 : How To Divide Exponents

If , then

Cannot be determined

Explanation:

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

Example Question #2 : How To Divide Exponents

If , which of the following is equal to ?

a6

a18

The answer cannot be determined from the above information

a

a4

a18

Explanation:

The numerator is simplified to  (by adding the exponents), then cube the result. a24/a6 can then be simplified to .

Example Question #3 : How To Divide Exponents

Explanation:

The easiest way to solve this is to simplify the fraction as much as possible. We can do this by factoring out the greatest common factor of the numerator and the denominator. In this case, the GCF is

Now, we can cancel out the  from the numerator and denominator and continue simplifying the expression.

Example Question #1 : Exponents

If (300)(400) = 12 * 10n, n =

7

2

3

12

4

4

Explanation:

(300)(400) = 120,000 or 12 * 104.

Example Question #1 : Exponents

(2x103) x (2x106) x (2x1012) = ?

8x1023

6x1023

6x1021

8x1021

8x1021

Explanation:

The three two multiply to become 8 and the powers of ten can be added to become 1021.

Example Question #1 : How To Multiply Exponents

Which of the following is equivalent to

Explanation:

and  can be multiplied together to give you  which is the first part of our answer. When you multiply exponents with the same base (in this case, ), you add the exponents. In this case,  should give us  because . The answer is

Example Question #1 : Exponents

If 3x = 27, then 22x = ?

32

9

64

3

8