Although we have different bases, we know that .

Therefore,

.

Finally, we factor out to get

.

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

Although we have different bases, we know that . As long as exponents are the same, you are allowed to break the base to its prime numbers. Next, we can factor .

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

m and n are both less than zero and thus negative integers, giving us _m_2 and _n_2 as perfect squares. The only perfect squares with a difference of 7 is 16 – 9, therefore m = –4 and n = –3.

When subtracting with exponents, we try to factor out some terms.

We can factor out to get

.

When we divide two polynomials with exponents, we subtract their exponents.

Remember that the question asks that all exponents be positive numbers. Therefore:

To simplify, we can rewrite the numerator using a common exponential base.

Now, we can factor out the numerator.

The eights cancel to give us our final answer.

Subtract the denominator exponent from the numerator's exponent, since they have the same base.

The correct answer can be found by subtracting exponents that have the same base. Whenever exponents with the same base are divided, you can subtract the exponent of the denominator from the exponent of the numerator as shown below to obtain the final answer:

You do not do anything with the y exponent because it has no identical bases.