# ACT Math : How to add exponents

## Example Questions

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

For all x, 2x2 times 12x3 equals...

14x5

24x6

14x6

0

24x5

24x5

Explanation:

You multiply the integers, then add the exponents on the x's, giving you 24x5.

### Example Question #31 : Exponential Operations

Multiply: 2x² * 3x

6x3

6x²

2x3

5x

5x3

6x3

Explanation:

When multiplying exponents you smiply add the exponents.

For 2x² times 3x, 2 times 3 is 6, and 2 + 1 is 3, so 2x² times 3x = 6x3

### Example Question #31 : Exponents

What is 23 + 22 ?

32

12

20

64

12

Explanation:

Using the rules of exponents, 23 + 22 = 8 + 4 = 12

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

Solve for  where:

9

2

5

3

1

1

Explanation:

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 #5 : How To Add Exponents

A particle travels 9 x 107 meters per second in a straight line for 12 x 10-6 seconds. How many meters has it traveled?

1.08 x 105

1.08 x 103

1.08 x 10

1.08

1.08 x 103

Explanation:

Multiplying the two numbers yields 1080. Expressed in scientific notation 1080 is 1.08 x 103.

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

Simplify: hn + h–2n

Explanation:

h–2n = 1/h2n

hn + h–2n = hn + 1/h2n

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

Simplify: 3y2 + 7y2 + 9y3 – y3 + y

10y2 + 9y3

19y11

10y4 + 8y6 + y

10y2 + 10y3 + y

10y2 + 8y3 + y

10y2 + 8y3 + y

Explanation:

Add the coefficients of similar variables (y, y2, 9y3)

3y2 + 7y2 + 9y3 – y3 + y =

(3 + 7)y2 + (9 – 1)y3 + y =

10y2 + 8y3 + y

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

Simplify the following:

Explanation:

When common variables have exponents that are multiplied, their exponents are added. So K* K4 =K(3+4) = K7.  And M6 * M2 = M(6+2) = M8. So the answer is K7/M8.

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

Solve for :

Explanation:

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 #41 : Exponential Operations

Simplify:  y3x4(yx3 + y2x2 + y15 + x22)

y4x7 + y5x6 + y18x4 + y3x26

2x4y4 + 7y15 + 7x22

y3x12 + y12x8 + y24x4 + y3x23

y3x12 + y6x8 + y45x4 + y3x88

y3x12 + y6x8 + y45 + x88

y4x7 + y5x6 + y18x4 + y3x26

Explanation:

When you multiply exponents, you add the common bases:

y4 x7 + y5x6 + y18x4 + y3x26

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