# ACT Math : Exponential Operations

## Example Questions

### Example Question #711 : Algebra

Simplify

.

Explanation:

This is just a matter of simply distributing this multiplication. Start by the basic distribution:

Now, you just add the exponents that are similar. Thus, you get:

### Example Question #712 : Algebra

Simplify the following:

None of these

Explanation:

The rule for multiplying exponents is

.

Using this, we see that

.

### Example Question #21 : Exponential Operations

The expression  is equivalent to which of the following?

None of these

Explanation:

The formula for multiplying exponents is

.

Using this, we see that

, and

.

### Example Question #22 : Exponential Operations

Simplify the following:

Explanation:

When two variables with exponents are multiplied, you can simplify the expression by adding the exponents together. In this particular problem, the correct answer is found by adding the exponents 5 and 5, yielding .

### Example Question #23 : Exponential Operations

Simplify the following to its simplest exponential expression:

Explanation:

When multiplying exponential expressions, the bases remain the same and the exponents are added. Thus, the answer to this question is .

### Example Question #24 : Exponential Operations

can be written as which of the following?

A.

B.

C.

A only

A, B and C

B and C

A and C

C only

A and C

Explanation:

B is not equivalent because...

A is equivalent because of a property of exponents meaning that . Consequently,

C is simply computing .

### Example Question #25 : Exponential Operations

Solve  when  and .

Explanation:

Substitute  for  and  for

Simplify:

### Example Question #26 : Exponential Operations

What is ?

Explanation:

When an exponent is raised to an exponent, you may simplify by multiplying the exponents together to make a new exponent. In this case,  becomes , which equals .

### Example Question #27 : Exponential Operations

Simplify:

Explanation:

When exponents with the same base are being multiplied, you may add the exponents together to create a new exponent.

In this case, you would add 6 and 4 to create 10 as the new exponent.

Keeping the same base, the answer becomes .

### Example Question #28 : Exponential Operations

Solve:  when  and .