# ACT Math : Exponential Ratios

## Example Questions

### Example Question #1 : How To Find A Ratio Of Exponents

If  and , then which of the following CANNOT be the value of ?

Explanation:

Even roots of numbers can either be positive or negative. Thus, x = +/- 5 and y = +/- 3. The possible values from x + y can therefore be:

(-5) + (-3) = -8

(-5) + 3 = -2

5 + (-3) = 2

5 + 3 = 8

### Example Question #1 : How To Find A Ratio Of Exponents

If  for all  not equal to 0, which of the following must be true?

Explanation:

Remember that

Since the problem states that , you can assume that

This shows that .

### Example Question #1 : Exponential Ratios

If  and are positive integers and , then what is the value of ?

Explanation:

43 = 64

Alternatively written, this is 4(4)(4) = 64 or 43 = 641.

Thus, m = 3 and n = 1.

m/n = 3/1 = 3.

### Example Question #1 : How To Find A Ratio Of Exponents

Write the following logarithm in expanded form:

Explanation:

### Example Question #21 : Algebra

If  and  are both rational numbers and , what is ?