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

## Example Questions

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

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

II, III, I, IV

I, IV, III, II

I, III, II, IV

IV, III, II, I

I, IV, II, III

I, III, II, IV

Explanation:

Solve for .

Explanation:

Since

Hence

Simplify:

Explanation:

### Example Question #1194 : Psat Mathematics

Solve for :

Explanation:

From the equation one can see that

Hence  must be equal to 25.

Evaluate:

Explanation:

Solve for .

Explanation:

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

and

Find

Explanation:

Hence the correct answer is .

### Example Question #1198 : Psat Mathematics

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 #1199 : Psat Mathematics

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?

12

125

27

36

40

27

Explanation:

The answer is 33 = 27

Solve for .