SAT Math : How to multiply exponents

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #41 : Exponents

Simplify into base .

Possible Answers:

Can't be simplified. 

Correct answer:

Explanation:

We need to get them to bases of . All of those bases derive from bases of  but raised to different powers.  is the same as  as anything raised to the first power is the same as its base. .

Next, . Since it's raised to the fourth power, let's make a proportion. 

.
The top represents the power of base . The bottom represents the power of base . When we cross-multiply, we have . So .

Finally,  is the same as . Let's do another proportion.

The top represents the power of base . The bottom represents the power of base .Wen we cross-mulltiply, we get . So .

With the same bases, we can add the exponents.

We have 

Example Question #41 : How To Multiply Exponents

can be stated as which of the following?

Possible Answers:

2 and 3

2 only

1 only

3 only

1 and 3

Correct answer:

2 and 3

Explanation:

This will test your knowledge of a specific exponential property: . Knowing that, 2 and 3 do come out to , while 1 comes out to only

Example Question #43 : How To Multiply Exponents

Simplify:

Possible Answers:

1

Correct answer:

Explanation:

When an exponent is raised to the power of another exponent, we multiply the exponents together.

 

For our x-value, the exponent will be 

For our y-value, the exponent will be 

Therefore, 

Example Question #452 : Algebra

Solve for  in terms of :

Possible Answers:

Correct answer:

Explanation:

Example Question #42 : Exponents

Evaluate 

Possible Answers:

Correct answer:

Explanation:

When multiplying exponents of the same base, we just add the exponents and keep the base the same.

Example Question #42 : How To Multiply Exponents

Evaluate 

Possible Answers:

Correct answer:

Explanation:

When multiplying exponents of the same base, we just add the exponents and keep the base the same.

Example Question #43 : How To Multiply Exponents

Evaluate 

Possible Answers:

Correct answer:

Explanation:

Although we have different bases, we know that  Therefore we have .

Example Question #44 : How To Multiply Exponents

Simplify

Possible Answers:

Correct answer:

Explanation:

Simplify the numerator

Pull an x out of each term in the numerator

The x in the numerator and the x in the denominator cancel

Example Question #45 : How To Multiply Exponents

Solve:

Possible Answers:

Correct answer:

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 6+12, to get a new exponent of 18:

Example Question #46 : How To Multiply Exponents

Solve:

Possible Answers:

Correct answer:

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:

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