### All PSAT Math Resources

## Example Questions

### Example Question #1 : How To Find An Exponent From A Rational Number

Which of the following lists the above quantities from least to greatest?

**Possible Answers:**

I, IV, III, II

I, III, II, IV

IV, III, II, I

II, III, I, IV

I, IV, II, III

**Correct answer:**

I, III, II, IV

Explanation:

### Example Question #2 : How To Find An Exponent From A Rational Number

Solve for .

**Possible Answers:**

**Correct answer:**

Explanation:

Since

Hence

### Example Question #3 : How To Find An Exponent From A Rational Number

Simplify:

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #1 : Exponential Ratios And Rational Numbers

Solve for :

**Possible Answers:**

**Correct answer:**

Explanation:

From the equation one can see that

Hence must be equal to 25.

### Example Question #5 : How To Find An Exponent From A Rational Number

Evaluate:

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #6 : How To Find An Exponent From A Rational Number

Solve for .

**Possible Answers:**

**Correct answer:**

Explanation:

### Example Question #7 : How To Find An Exponent From A Rational Number

and

Find

**Possible Answers:**

**Correct answer:**

Explanation:

Hence the correct answer is .

### Example Question #8 : How To Find An Exponent From A Rational Number

Solve for .

**Possible Answers:**

**Correct answer:**

Explanation:

Use the rules of logarithms to combine terms.

Hence,

By fatoring we get

Hence .

However, you cannot take the logarithm of a negative number. Thus, the only value for is .

### Example Question #1 : Exponents And Rational Numbers

If a piece of pie is cut into 3 sections, and each of those pieces is further cut into three sections, then those pieces are cut into three sections, how many (tiny) pieces of pie are there?

**Possible Answers:**

27

40

12

36

125

**Correct answer:**

27

Explanation:

The answer is 3^{3} = 27

### Example Question #9 : How To Find An Exponent From A Rational Number

Solve for .

**Possible Answers:**

**Correct answer:**

Explanation: