How to multiply exponents - GRE Quantitative Reasoning

(y2)(y4) = y2+4 = y6

Plug in two different values for y.

Plug in y = 1: y8 = y6

Plug in y = 2: y8 > y6

Since the results differ, the relationship cannot be determined from the information given.

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.

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.

The two quantites are equal. To take the exponent of an exponent, the two exponents should be multiplied.

(23 )2 or 23*2 = 64

(22 )3 or 22*3 = 64

Both quantities equal 64, so the two quantities are equal.

Can be simplified to:

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).

To compare these expressions more easily, we'll change the first expression to have in front. We'll do this by factoring out 25 (that is, ) from 850, then using the fact that .

When we combine like terms, we can see that . The two terms are therefore both equal to the same value.

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.

First, multiply inside the parentheses: .

Then raise to the 7th power: .

To solve this problem, we must first understand some of the basic concepts of exponents. When multiplying exponents with the same base, one would simply add the powers together with the same base to obtain the result. For example, .

When raising exponents to a certain power, one would simply multiply the power the exponent is being raised to with the exponent itself to obtain the new exponent. The base also gets raised to the same power as it normally would and the new exponent gets put on afterward. For example .

Now that we have covered the basic concepts of exponent manipulation, we can now solve the problem. The top part of the expression give to us is . As we have stated before, when an exponent is raised to a certain power, you simply multiply the power and the exponent together. This results in .

The new expression becomes .

Solving for the denominator of the equation, we previously stated that when multiplying exponents together with the same base, we simply add the exponents together and keep the same base. Therefore .

The new expression becomes , however , therefore the expression becomes .

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.

(y2)(y4) = y2+4 = y6

Plug in two different values for y.

Plug in y = 1: y8 = y6

Plug in y = 2: y8 > y6

Since the results differ, the relationship cannot be determined from the information given.

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.

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.

The two quantites are equal. To take the exponent of an exponent, the two exponents should be multiplied.

(23 )2 or 23*2 = 64

(22 )3 or 22*3 = 64

Both quantities equal 64, so the two quantities are equal.