PSAT Math : Exponents

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #121 : Exponents

Possible Answers:

Correct answer:

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

\dpi{100} \small \frac{20x^{4}y^{-3}z^{2}}{5z^{-1}y^{2}x^{2}}=

Possible Answers:

\dpi{100} \small 15x^{-2}y^{-2}z^{-2}

\dpi{100} \small {4x^{5}y^{-2}}

\dpi{100} \small 15x^{2}y^{2}z^{2}

\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}

None

Correct answer:

\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}

Explanation:

Divide the coefficients and subtract the exponents.

Example Question #1 : How To Divide Exponents

Which of the following is equal to the expression Equationgre, where  

xyz ≠ 0?

Possible Answers:

z/(xy)

xyz

z

1/y

xy

Correct answer:

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

 

Possible Answers:

Cannot be determined

Correct answer:

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 ?

Possible Answers:

a6

a18

The answer cannot be determined from the above information

a

a4

Correct answer:

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

Possible Answers:

\dpi{100} \small 343

\dpi{100} \small 42

\dpi{100} \small 28

\dpi{100} \small 7

\dpi{100} \small 49

Correct answer:

\dpi{100} \small 7

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 =

Possible Answers:

7

2

3

12

4

Correct answer:

4

Explanation:

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

Example Question #1 : Exponents

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

Possible Answers:

8x1023

6x1023

6x1021

8x1021

Correct answer:

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 

Possible Answers:

Correct answer:

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 = ?

Possible Answers:

32

9

64

3

8

Correct answer:

64

Explanation:
  1. Solve for x in 3x = 27. x = 3 because 3 * 3 * 3 = 27.
  2. Since x = 3, one can substitute x for 3 in 22x 
  3. Now, the expression is 22*3
  4. This expression can be interpreted as 22 * 2* 22. Since 22 = 4, the expression can be simplified to become 4 * 4 * 4 = 64.
  5. You can also multiply the powers to simplify the expression. When you multiply the powers, you get 26, or 2 * 2 * 2 * 2 * 2 * 2
  6. 2= 64.
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