### All PSAT Math Resources

## Example Questions

### Example Question #121 : Exponents

**Possible Answers:**

**Correct answer:**

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

**Possible Answers:**

None

**Correct answer:**

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?

**Possible Answers:**

z/(xy)

xyz

z

1/y

xy

**Correct answer:**

1/y

(xy)^{4} can be rewritten as x^{4}y^{4} and z^{0} = 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:**

Start by simplifying the numerator and denominator separately. In the numerator, (c^{3})^{2} is equal to c^{6}. In the denominator, c^{2 }* c^{4} equals c^{6} as well. Dividing the numerator by the denominator, c^{6}/c^{6}, 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:**

a^{6}

a^{18}

The answer cannot be determined from the above information

a

a^{4}

**Correct answer:**

a^{18}

The numerator is simplified to (by adding the exponents), then cube the result. a^{24}/a^{6} can then be simplified to .

### Example Question #3 : How To Divide Exponents

**Possible Answers:**

**Correct answer:**

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 * 10* ^{n}*,

*n*=

**Possible Answers:**

7

2

3

12

4

**Correct answer:**

4

(300)(400) = 120,000 or 12 * 10^{4}.

### Example Question #1 : Exponents

(2x10^{3}) x (2x10^{6}) x (2x10^{12}) = ?

**Possible Answers:**

8x10^{23}

6x10^{23}

6x10^{21}

8x10^{21}

**Correct answer:**

8x10^{21}

The three two multiply to become 8 and the powers of ten can be added to become 10^{21}.

### Example Question #1 : How To Multiply Exponents

Which of the following is equivalent to

**Possible Answers:**

**Correct answer:**

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 3^{x} = 27, then 2^{2x }= ?

**Possible Answers:**

32

9

64

3

8

**Correct answer:**

64

- Solve for x in 3
^{x}= 27. x = 3 because 3 * 3 * 3 = 27. - Since x = 3, one can substitute x for 3 in 2
^{2x } - Now, the expression is 2
^{2*3} - This expression can be interpreted as 2
^{2 * }2^{2 }* 2^{2}. Since 2^{2 }= 4, the expression can be simplified to become 4 * 4 * 4 = 64. - You can also
*multiply the powers*to simplify the expression. When you*multiply the powers*, you get 2^{6}, or 2 * 2 * 2 * 2 * 2 * 2 - 2
^{6 }= 64.

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