### All ACT Math Resources

## Example Questions

### Example Question #31 : Exponential Operations

Simplify:

**Possible Answers:**

**Correct answer:**

When an exponent is raised to an exponent, multiply the two together to yield a new exponent, and attach that exponent to the original base.

In this case, multiply and to yield , and your answer is .

### Example Question #32 : Exponential Operations

Solve: when .

**Possible Answers:**

**Correct answer:**

When an exponent is raised to another exponent, you may multiply them together to find the exponent of the answer. Attach that exponent to the original base, and that is the solution.

In this particular problem, multiply by , which yields as the final exponent. This makes .

Now, substitute for : .

### Example Question #33 : Exponential Operations

What is

?

**Possible Answers:**

**Correct answer:**

Negative exponents are reciprocals. Do not change the sign to negative.

The variables with negative exponents can be written as their reciprocals.

,

Multiplying these new forms together gives,

From here, simplify by factoring out a common factor from the numerator and denominator.

### Example Question #34 : Exponential Operations

Simplify the following:

**Possible Answers:**

**Correct answer:**

To solve, simply distribute the outer exponent. When you have an exponent to an exponent, you multiply their values. Thus,

### Example Question #35 : Exponential Operations

Which of the following is a value of x that satisfies

**Possible Answers:**

1

2

0

4

3

**Correct answer:**

2

This question incorporates properties of exponents. The best way to solve this problem is to establish the same base for all of the terms.

Now use the properties of exponents to simplify the left side of the equation. When exponential terms with the same base are multiplied, the exponents are added.

Now, with the left side simplified, set that equal to .

Since each side has one term with the same base, simply set the exponents equal to each other and solve for x.

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

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

**Possible Answers:**

14*x*^{5}

24*x*^{6}

14*x*^{6}

0

24*x*^{5}

**Correct answer:**

24*x*^{5}

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

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

Multiply: 2*x*² * 3x

**Possible Answers:**

6*x*²

6*x*^{3}

5*x*

5*x*^{3}

2*x*^{3}

**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 #3 : 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 #4 : How To Add Exponents

Solve for where:

**Possible Answers:**

5

9

3

1

2

**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 #5 : 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^{5}

1.08 x 10^{3}

1.08 x 10

1.08

**Correct answer:**

1.08 x 10^{3}

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

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