### All PSAT Math Resources

## Example Questions

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

**Possible Answers:**

**Correct answer:**

Explanation:

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

Rationalize the denominator:

**Possible Answers:**

**Correct answer:**

Explanation:

The conjugate of is .

Now multiply both the numerator and the denominator by

and you get:

Hence we get

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

Solve for :

**Possible Answers:**

**Correct answer:**

Explanation:

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

Solve for .

**Possible Answers:**

**Correct answer:**

Explanation:

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

If,

What does

**Possible Answers:**

**Correct answer:**

Explanation:

If ,

then .

### Example Question #106 : Exponents

**Possible Answers:**

**Correct answer:**

Explanation:

From the equation in the problem statement

Now squaring both sides we get

this is a quadratic equation which equals

and the factors of this equation are

This gives us .

However, if we plug these solutions back into the original equation, does not create an equality. Therefore, is an extraneous solution.

### Example Question #107 : Exponents

For some positive integer , if , what is the value of ?

**Possible Answers:**

**Correct answer:**

Explanation:

If , then must equal 3 (Note that cannot be -3 because you need it to be positive.

Now, plug into the new equation :

Josh

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