Exponential Operations

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SAT Math › Exponential Operations

Questions 1 - 10
1

Simplify:

Explanation

Although we have different bases, we know that .

Therefore,

.

Finally, we factor out to get

.

2

Simplify:

Explanation

When multiplying exponents, we just add the exponents while keeping the base the same.

3

Solve:

Explanation

When multiplying expressions with the same variable, combine terms by adding the exponents, while leaving the variable unchanged. For this problem, we do that by adding 2+1, to get a new exponent of 3:

4

Explanation

When multplying exponents, we need to make sure we have the same base.

Since we do, all we have to do is add the exponents.

The answer is .

5

Evaluate

Explanation

When adding exponents, we don't multiply the exponents but we try to factor to see if we simplify the addition problem. In this case, we can simplify it by factoring . We get .

6

Given , what is the value of ?

7

11

3

9

5

Explanation

Express as a power of ; that is: .

Then .

Using the properties of exponents, .

Therefore, , so .

7

Given , what is the value of ?

7

11

3

9

5

Explanation

Express as a power of ; that is: .

Then .

Using the properties of exponents, .

Therefore, , so .

8

Simplify:

Explanation

When adding exponents, you want to factor out to make solving the question easier.

We can factor out to get

.

Now we can add exponents and therefore our answer is

.

9

Evaluate

Explanation

When adding exponents, we don't multiply the exponents but we try to factor to see if we simplify the addition problem. In this case, we can simplify it by factoring . We get .

10

Simplify:

Explanation

When we multiply two polynomials with exponents, we add their exponents together. Therefore,

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