How to subtract exponents

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

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.

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 .

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,

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.

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:

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,