### All PSAT Math Resources

## Example Questions

### Example Question #11 : Exponents

(*x*^{3})^{2} * *x ^{–}*

^{2}=

**Possible Answers:**

*x*^{2}

*x*^{4}

*x*^{6}

*x*

*x ^{–}*

^{4}

**Correct answer:**

*x*^{4}

When an exponent is raised to a power, we multiply. But when two exponents with the same base are multiplied, we add them. So (*x*^{3})^{2} = *x*^{3*2} = *x*^{6}. Then (*x*^{3})^{2} * *x ^{–}*

^{2}=

*x*

^{6}*

*x*

^{–}^{2}=

*x*

^{6 – 2}=

*x*

^{4}.

### Example Question #11 : Exponents

If , then which of the following is equivalent to ?

**Possible Answers:**

6^7

6^4

6^8

6^6

**Correct answer:**

We can break up the equation into two smaller equations involving only *x* and *y*. Then, once we solve for *x* and *y*, we can find the value of .

### Example Question #41 : Exponents

If which of the following must be true?

I.

II.

III.

**Possible Answers:**

I

III

None

All

II

**Correct answer:**

None

must be negative because it has an odd power and and have even powers above. But and could be positive or negative, so none of the scenarios has to be true.

### Example Question #11 : How To Multiply Exponents

**Possible Answers:**

**Correct answer:**

Hence the correct answer will be

### Example Question #11 : Exponents

Solve for :

**Possible Answers:**

**Correct answer:**

If

Then

and

Hence

### Example Question #51 : Exponents

**Possible Answers:**

**Correct answer:**

(x^{3}y^{6}z)(x^{2}yz^{3})

The paraentheses are irrelevant. Rearrange to combine like terms.

x^{3}x^{2}y^{6}y^{1}z^{1}z^{3}

When you multiply variables with exponents, simply add the exponents together.

x^{3+2 }y^{6+1 }z^{1+3}

x^{5}y^{7}z^{4}

### Example Question #51 : Exponents

If an original bacteria colony contains six organisms, and triples every hour, how many organisms are there after 7 hours?

**Possible Answers:**

**Correct answer:**

To find the answer we can apply the equation of population where is the number of hours.

### Example Question #491 : Algebra

Simplify:

**Possible Answers:**

**Correct answer:**

Use the distributive property: . When we multiply variables with exponents, we keep the same base and add the exponents:

### Example Question #12 : Exponents

Simplify:

**Possible Answers:**

**Correct answer:**

We cannot combine with , so .

### Example Question #492 : Algebra

If , then what is the value of ?

**Possible Answers:**

**Correct answer:**

c^{4} is equal to (c^{2})(c^{2}).

We know c^{2} = 15. Plugging in this value gives us c^{4} = (15)(15) = 225.

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