When we have two identical numbers, each raised to an exponent, and multiplied together, we add the exponents together:

xaxb = xa+b

This means that (0.5)3(0.5)3 = (0.5)3+3 = (0.5)6

Because 0.5 is between 0 and 1, we know that when it is multipled by itself, it decreases in value. Example: 0.5 * 0.5 = 0.25. 0.5 * 0.5 * 0.5 = 0.125. Etc.

Thus, (0.5)6 > (0.5)7

Answer: The relationship cannot be determined from the information provided.

Explanation: The best thing to do here is to notice that quantity A is composed of two complex terms with odd exponents. Odd powers result in negative results when their base is negative. Thus quantity A will be negative when either x or y (but not both) is negative. Otherwise, quantity A will be positive. Quantity B, however, has two even exponents, meaning that it will always be positive. Thus, sometimes Quantity A will be greater and sometimes Quantity B will be greater. Thus the answer is that the relationship cannot be determined.

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

First let's look at Quantity B:

(x/3)3 = _x_3/27. Now both columns have an _x_3 so we can cancel it from both terms. Therefore we're now comparing 1/3 in Quantity A to 1/27 in Quantity B. 1/3 is the larger fraction so Quantity A is greater.

However, if , then the two quantities would both equal 0. Thus, since the two quantities can have different relationships based on the value of , we cannot determine the relationship from the information given.

First, multiply inside the parentheses: .

Then raise to the 7th power: .

Remember, we add exponents when their bases are multiplied, and multiply exponents when one is raised to the power of another. Negative exponents flip to the denominator (presuming they originally appear in the numerator).

Can be simplified to:

is always equal to ; therefore, 5 raised to 4 times 5 raised to 5 must equal 5 raised to 9.

is always equal to . Therefore, 5 raised to 9, raised to 20 must equal 5 raised to 180.