# PSAT Math : How to find a rational number from an exponent

## Example Questions

### Example Question #232 : Exponents       Explanation: ### Example Question #1 : How To Find A Rational Number From An Exponent

Rationalize the denominator:       Explanation:

The conjugate of is .

Now multiply both the numerator and the denominator by and you get:  Hence we get ### Example Question #234 : Exponents

Solve for :       Explanation:   ### Example Question #235 : Exponents

Solve for .       Explanation:  ### Example Question #1 : How To Find A Rational Number From An Exponent

If, What does       Explanation:

If ,

then .

### Example Question #237 : Exponents       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 #1 : How To Find A Rational Number From An Exponent

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

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

Now, plug into the new equation :    