### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Subtract Exponents

Reduce to simplest form.

**Possible Answers:**

**Correct answer:**

When dividing terms with the same bases but different exponents, you will need to subtract all the pertinent exponents.

becomes ,

becomes ,

and stays the same because there is no other z term to combine with it.

Thus resulting in:

### Example Question #51 : Exponents

Simplify: 3^{2} * (4^{23} - 4^{21})

**Possible Answers:**

3^3 * 4^21 * 5

4^4

3^21

3^3 * 4^21

None of the other answers

**Correct answer:**

3^3 * 4^21 * 5

Begin by noting that the group (4^{23} - 4^{21}) has a common factor, namely 4^{21}. You can treat this like any other constant or variable and factor it out. That would give you: 4^{21}(4^{2} - 1). Therefore, we know that:

3^{2} * (4^{23} - 4^{21}) = 3^{2} * 4^{21}(4^{2} - 1)

Now, 4^{2} - 1 = 16 - 1 = 15 = 5 * 3. Replace that in the original:

3^{2} * 4^{21}(4^{2} - 1) = 3^{2} * 4^{21}(3 * 5)

Combining multiples withe same base, you get:

3^{3} * 4^{21} * 5

### Example Question #3 : How To Subtract Exponents

Simplify. Leave no negative exponents in the final answer.

**Possible Answers:**

None of these are the correct answer.

**Correct answer:**

The first step in the problem is to combine like terms in the numerator, remembering that :

Next, we resolve the numerator, using and :

Lastly, simplify the negative exponent using

Thus,

### Example Question #4 : How To Subtract Exponents

Simplify to remove fractions:

**Possible Answers:**

None of these are correct.

**Correct answer:**

The first step is to simplify each fraction by dividing like terms, remembering that , to get:

Next, combine using multiplication and the rule :

Since the problem specifies that we must avoid fractions, we will not eliminate the negative exponents.

So,

### Example Question #5 : How To Subtract Exponents

Simplify the following:

**Possible Answers:**

**Correct answer:**

When dividing exponential expressions with the same base, subtract the exponents. In this problem, the exponents are and . When subtracted, the result is . Thus, the correct answer is .

### Example Question #6 : How To Subtract Exponents

can be written as which of the following?

A.

B.

C.

**Possible Answers:**

A and C

C only

A, B and C

B and C

B only

**Correct answer:**

B and C

A is not equivalent because exponents in denominators mean subtraction of exponents and not division of them. Furthermore, A, when computed, comes out to instead of .

B is equivalent by the aforementioned exponential property, while C is simply computing the expression.

### Example Question #7 : How To Subtract Exponents

Simplify:

**Possible Answers:**

**Correct answer:**

When two exponents with the same base are being divided, subtract the exponent of the denominator from the exponent of the numerator to yield a new exponent. Attach that exponent to the base, and that is your answer.

In this case, subtract from . That yields as the new exponent and as the answer.