How to add exponents

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SAT Math › How to add exponents

Questions 1 - 10
1

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

.

2

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 .

3

Simplify:

Explanation

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

4

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 .

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

Evaluate

Explanation

Although we have different bases, we do know . Therefore our expression is . Remember to apply the power rule of exponents. Then, now we can factor .

7

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

y4x7 + y5x6 + y18x4 + y3x26

y3x12 + y6x8 + y45x4 + y3x88

y3x12 + y6x8 + y45 + x88

2x4y4 + 7y15 + 7x22

y3x12 + y12x8 + y24x4 + y3x23

Explanation

When you multiply exponents, you add the common bases:

y4 x7 + y5x6 + y18x4 + y3x26

8

Evaluate:

Explanation

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

we can factor out to get

.

We have the same base so we just apply the exponent rule for multiplication to get

.

9

Which of the following is equivalent to ?

Explanation

Although each base is different, we can convert them to a common base of

We know

,

,

and

.

Remember to apply the power rule of exponents.

Therefore we have

.

We can factor out to get

.

10

If , what is the value of ?

Explanation

Since the base is 5 for each term, we can say 2 + n =12. Solve the equation for n by subtracting 2 from both sides to get n = 10.

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