### All ACT Math Resources

## Example Questions

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

Simplify

**Possible Answers:**

None of the answers are correct

**Correct answer:**

When working with polynomials, dividing is the same as multiplying by the reciprocal. After multiplying, simplify. The correct answer for division is

and the correct answer for multiplication is

### Example Question #61 : Exponential Operations

Simplify:

**Possible Answers:**

**Correct answer:**

To simply exponents in a fraction, subtract the exponent for each variable in the denominator from the exponent in the numerator. This will leave you with

or

### Example Question #62 : Exponential Operations

What is the value of *m* where:

**Possible Answers:**

2

1

6

4

-2

**Correct answer:**

2

If n=4, then 64^{(4/12)}=64^{(1/3)}=4. Then, 4=m4^{(1+m)/(m+4)}. If 2 is substituted for *m*, then 4=24^{(1+2)/(2+4)}=24^{1/2}=2√4=22=4.

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

Simplify the following:

**Possible Answers:**

x^{7/3}

1/x^{4}

Cannot be done

x^{4}

**Correct answer:**

x^{4}

These exponents have the same base, x, so they can be divided. To divide them, you take the exponent value in the numerator (the top exponent) and subtract the exponent value of the denominator (the bottom exponent). Here that means we take 7 – 3 so our answer is x^{4}.

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

Simplify:

**Possible Answers:**

**Correct answer:**

Use rule for multiplying exponents to simplify the numerator.

Use rule for dividing exponents to simplify.

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

Simplify:

**Possible Answers:**

**Correct answer:**

Simplify:

Step 1: Simplify the fraction. When dividing exponents subtract the exponents on the bottom from the exponents on the top.

Step 2: Distribute the exponent. When raising an exponent to a power, multiply them together.

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

Simplify

**Possible Answers:**

None

**Correct answer:**

Divide the coefficients and subtract the exponents.

### Example Question #1 : Exponential Operations

Which of the following is equal to the expression , where

xyz ≠ 0?

**Possible Answers:**

1/y

xy

xyz

z

z/(xy)

**Correct answer:**

1/y

(xy)^{4} can be rewritten as x^{4}y^{4} and z^{0} = 1 because a number to the zero power equals 1. After simplifying, you get 1/y.

### Example Question #2 : Exponential Operations

If , then

**Possible Answers:**

Cannot be determined

**Correct answer:**

Start by simplifying the numerator and denominator separately. In the numerator, (c^{3})^{2} is equal to c^{6}. In the denominator, c^{2 }* c^{4} equals c^{6} as well. Dividing the numerator by the denominator, c^{6}/c^{6}, gives an answer of 1, because the numerator and the denominator are the equivalent.

### Example Question #4 : Exponential Operations

If , which of the following is equal to ?

**Possible Answers:**

a^{4}

The answer cannot be determined from the above information

a

a^{6}

a^{18}

**Correct answer:**

a^{18}

The numerator is simplified to (by adding the exponents), then cube the result. a^{24}/a^{6} can then be simplified to .

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