When two variables with exponents are multiplied, you can simplify the expression by adding the exponents together. In this particular problem, the correct answer is found by adding the exponents 5 and 5, yielding .

Simplifying the equation gives b6/(b3+x) = b5.

In order to satisfy this case, x must be equal to –2.

7/8 is being raised to the 5th power and to the 1/2 power at the same time. We multiply these to find n.

Let's do each of these separately:

x3 * 2x4 * 5y = 2 * 5 * x3 * x4 * y = 10 * x7 * y = 10x7y

4y2 + 3y2 = 7y2

Now, rewrite what we have so far:

(10x7y + 7y2)/y

There are several options for reducing this. Remember that when we divide, we can "distribute" the denominator through to each member. That means we can rewrite this as:

(10x7y)/y + (7y2)/y

Subtract the y exponents values in each term to get:

10x7 + 7y

We are given an expression with a power to a power to a power. Using rules of exponents, we take the exponents and multiply each of them together.

Substitute for and for :

Simplify:

The formula for multiplying exponents is

.

Using this, we see that

, and

.

To tackle this problem we must understand the concept of exponents in fractions and how to cancel and move them.

To move any variable or number from the numerator to the denominator or vice versa, you must negate the exponent. i.e. in the numerator would become in the denominator. These two expression are equivalent. You should strive to make all exponents positive initially before applying the next rule to simplify.

Cancelling variables with a similar base is an easy way to simplify. Add or subtract the exponents depending on their relationship in a fraction.

Ex. or 1.

Ex. . --> this can be more easily understood if you break down the . which then can be moved around to form, . After the cancels to form 1, we have or just . This can be applied for all numerical or abstract values of exponents for a given variable, such as , or .

Knowing these rules, we can tackle the problem.

To begin we will pick a variable to start with, thereby breaking down the problem into three smaller chunks. First we will start with the variable . . Because the numerator has a negative exponent, we will move it down to the denominator: . This simplifies to as multiplying any common variables with exponents is found by addition of the exponents atop the original variable. The variable part of this problem is .

We move to the section of the problem: . This is similar to our above, instead with larger numerical exponents. . The section cancels, leaving us with or .

Now to the section. We simply have on top. Applying the first rule above, we just move it to the denominator with the switching of the sign. Our result is .

Combining all the sections together we have .

More beautifully written it looks like .

You can simplify it into (_x_3)(_x_3) = _x_6