### All ACT Math Resources

## Example Questions

### Example Question #1 : Exponential Ratios

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

**Possible Answers:**

**Correct answer:**

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 #2 : Exponential Ratios

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

**Possible Answers:**

**Correct answer:**

Remember that

Since the problem states that , you can assume that

This shows that .

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

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

**Possible Answers:**

**Correct answer:**

4^{3 }= 64

Alternatively written, this is 4(4)(4) = 64 or 4^{3 }= 64^{1.}

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:

**Possible Answers:**

**Correct answer:**

### Example Question #4 : Exponential Ratios

If and are both rational numbers and , what is ?

**Possible Answers:**

**Correct answer:**

This question is asking you for the ratio of m to n. To figure it out, the easiest way is to figure out when 4 to an exponent equals 8 to an exponent. The easiest way to do that is to list the first few results of 4 to an exponent and 8 to an exponent and check to see if any match up, before resorting to more drastic means of finding a formula.

And, would you look at that. . Therefore, .

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