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

## Example Questions

### Example Question #10 : Exponents And Rational Numbers Which of the following lists the above quantities from least to greatest?

II, III, I, IV

I, III, II, IV

I, IV, II, III

IV, III, II, I

I, IV, III, II

I, III, II, IV

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

Solve for .       Explanation:

Since Hence ### Example Question #2 : Exponents And Rational Numbers

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

Solve for :       Explanation:

From the equation one can see that Hence must be equal to 25.

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

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

Solve for .       Explanation: ### Example Question #631 : Algebra and Find       Explanation: Hence the correct answer is .

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

Solve for .       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 #11 : Exponential Ratios 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?

36

40

27

12

125

27

Explanation:

The answer is 33 = 27

### Example Question #2 : Exponents And Rational Numbers

Solve for .          