### All ACT Math Resources

## Example Questions

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

For all *x*, 2*x*^{2} times 12*x*^{3} equals...

**Possible Answers:**

0

14*x*^{5}

24*x*^{5}

14*x*^{6}

24*x*^{6}

**Correct answer:**

24*x*^{5}

You multiply the integers, then add the exponents on the *x*'s, giving you 24*x*^{5}.

### Example Question #31 : Exponential Operations

Multiply: 2*x*² * 3x

**Possible Answers:**

6*x*^{3}

6*x*²

2*x*^{3}

5*x*^{3}

5*x*

**Correct answer:**

6*x*^{3}

When multiplying exponents you smiply add the exponents.

For 2*x*² times 3*x*, 2 times 3 is 6, and 2 + 1 is 3, so 2*x*² times 3*x* = 6*x*^{3}

### Example Question #2 : How To Add Exponents

What is 2^{3} + 2^{2 }?

**Possible Answers:**

20

32

12

64

**Correct answer:**

12

Using the rules of exponents, 2^{3} + 2^{2 }= 8 + 4 = 12

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

Solve for where:

**Possible Answers:**

5

1

2

9

3

**Correct answer:**

1

The only value of x where the two equations equal each other is 1. All you have to do is substitute the answer choices in for x.

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

A particle travels 9 x 10^{7} meters per second in a straight line for 12 x 10^{-6} seconds. How many meters has it traveled?

**Possible Answers:**

1.08 x 10

1.08

1.08 x 10^{3}

1.08 x 10^{5}

**Correct answer:**

1.08 x 10^{3}

Multiplying the two numbers yields 1080. Expressed in scientific notation 1080 is 1.08 x 10^{3}.

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

Simplify: h^{n} + h^{–2n }

**Possible Answers:**

^{}

^{}

^{}

**Correct answer:**

^{}

h^{–2n }= 1/h^{2n}

h^{n} + h^{–2n }= h^{n} + 1/h^{2n}

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

Simplify: 3y^{2} + 7y^{2} + 9y^{3} – y^{3} + y

**Possible Answers:**

19y^{11}

10y^{2} + 10y^{3} + y

10y^{4} + 8y^{6} + y

10y^{2} + 8y^{3} + y

10y^{2} + 9y^{3}

**Correct answer:**

10y^{2} + 8y^{3} + y

Add the coefficients of similar variables (y, y^{2}, 9y^{3})

3y^{2} + 7y^{2} + 9y^{3} – y^{3} + y =

(3 + 7)y^{2} + (9 – 1)y^{3} + y =

10y^{2} + 8y^{3} + y

### Example Question #2 : How To Add Exponents

Simplify the following:

**Possible Answers:**

**Correct answer:**

When common variables have exponents that are multiplied, their exponents are added. So *K*^{3 }* *K*^{4} =*K*^{(}^{3+4)} = *K*^{7}. And *M*^{6} * *M*^{2} = *M*^{(6+2)} = *M*^{8}. So the answer is *K*^{7}/*M*^{8}.

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

Solve for :

**Possible Answers:**

**Correct answer:**

First, reduce all values to a common base using properties of exponents.

Plugging back into the equation-

Using the formula

We can reduce our equation to

So,

### Example Question #8 : Exponential Operations

Simplify: y^{3}x^{4}(yx^{3} + y^{2}x^{2} + y^{15} + x^{22})

**Possible Answers:**

2x^{4}y^{4} + 7y^{15} + 7x^{22}

y^{3}x^{12} + y^{6}x^{8} + y^{45}x^{4} + y^{3}x^{88}

y^{4}x^{7} + y^{5}x^{6} + y^{18}x^{4} + y^{3}x^{26}

y^{3}x^{12} + y^{12}x^{8} + y^{24}x^{4} + y^{3}x^{23}

y^{3}x^{12} + y^{6}x^{8} + y^{45} + x^{88}

**Correct answer:**

y^{4}x^{7} + y^{5}x^{6} + y^{18}x^{4} + y^{3}x^{26}

When you multiply exponents, you add the common bases:

y^{4} x^{7} + y^{5}x^{6} + y^{18}x^{4} + y^{3}x^{26}