How to add and subtract exponents with different bases

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Reduce 

Correct answer:

Explanation:

When dividing terms with the same bases but different exponents, you will need to subtract all the pertinent exponents.

 becomes ,

 becomes ,

and  stays the same because there is no other z term to combine with it.

Thus resulting in:

Simplify: 32 * (423 - 421)

Possible Answers:

3^3 * 4^21 * 5

4^4

3^3 * 4^21

None of the other answers

3^21

Correct answer:

3^3 * 4^21 * 5

Explanation:

Begin by noting that the group (423 - 421) has a common factor, namely 421.  You can treat this like any other constant or variable and factor it out.  That would give you: 421(42 - 1). Therefore, we know that:

32 * (423 - 421) = 32 * 421(42 - 1)

Now, 42 - 1 = 16 - 1 = 15 = 5 * 3.  Replace that in the original:

32 * 421(42 - 1) = 32 * 421(3 * 5)

Combining multiples withe same base, you get:

33 * 421 * 5

Simplify. Leave no negative exponents in the final answer.

Possible Answers:

None of these are the correct answer.

Correct answer:

Explanation:

The first step in the problem is to combine like terms in the numerator, remembering that :

Next, we resolve the numerator, using  and : 

Lastly, simplify the negative exponent using 

 Thus,  

Simplify to remove fractions:

Possible Answers:

None of these are correct.

Correct answer:

Explanation:

The first step is to simplify each fraction by dividing like terms, remembering that , to get: 

Next, combine using multiplication and the rule :

Since the problem specifies that we must avoid fractions, we will not eliminate the negative exponents.

So, 

Simplify the following: 

Correct answer:

Explanation:

When dividing exponential expressions with the same base, subtract the exponents. In this problem, the exponents are  and . When subtracted, the result is . Thus, the correct answer is .

 can be written as which of the following?

A.

B.

C.

Possible Answers:

B and C

A, B and C

A and C

C only

B only

Explanation:

A is not equivalent because exponents in denominators mean subtraction of exponents and not division of them. Furthermore, A, when computed, comes out to instead of .

B is equivalent by the aforementioned exponential property, while C is simply computing the expression.

Simplify: 

Correct answer:

Explanation:

When two exponents with the same base are being divided, subtract the exponent of the denominator from the exponent of the numerator to yield a new exponent. Attach that exponent to the base, and that is your answer. 

In this case, subtract  from . That yields  as the new exponent and  as the answer.

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