How to subtract exponents - GRE Quantitative Reasoning

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

We can solve this without actually doing the math. Let's look at 64 vs 52. 64 is clearly bigger. Now let's look at 32 vs 42. 32 is clearly smaller. Then, bigger – smaller is greater than smaller – bigger, so Quantity A is bigger.

The first thing to note is the relationship between (–b) and (1 – b):

(–b) < (1 – b) because (–b) + 1 = (1 – b).

Now when b > 1, (1 – b) < 0 and –b < 0. Therefore (–b) < (1 – b) < 0.

Raising a negative number to an odd power produces another negative number.

Thus (–b)a < (1 – b)a < 0.

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

We can solve this without actually doing the math. Let's look at 64 vs 52. 64 is clearly bigger. Now let's look at 32 vs 42. 32 is clearly smaller. Then, bigger – smaller is greater than smaller – bigger, so Quantity A is bigger.

The first thing to note is the relationship between (–b) and (1 – b):

(–b) < (1 – b) because (–b) + 1 = (1 – b).

Now when b > 1, (1 – b) < 0 and –b < 0. Therefore (–b) < (1 – b) < 0.

Raising a negative number to an odd power produces another negative number.

Thus (–b)a < (1 – b)a < 0.

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

We can solve this without actually doing the math. Let's look at 64 vs 52. 64 is clearly bigger. Now let's look at 32 vs 42. 32 is clearly smaller. Then, bigger – smaller is greater than smaller – bigger, so Quantity A is bigger.

The first thing to note is the relationship between (–b) and (1 – b):

(–b) < (1 – b) because (–b) + 1 = (1 – b).

Now when b > 1, (1 – b) < 0 and –b < 0. Therefore (–b) < (1 – b) < 0.

Raising a negative number to an odd power produces another negative number.

Thus (–b)a < (1 – b)a < 0.

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

We can solve this without actually doing the math. Let's look at 64 vs 52. 64 is clearly bigger. Now let's look at 32 vs 42. 32 is clearly smaller. Then, bigger – smaller is greater than smaller – bigger, so Quantity A is bigger.

The first thing to note is the relationship between (–b) and (1 – b):

(–b) < (1 – b) because (–b) + 1 = (1 – b).

Now when b > 1, (1 – b) < 0 and –b < 0. Therefore (–b) < (1 – b) < 0.

Raising a negative number to an odd power produces another negative number.

Thus (–b)a < (1 – b)a < 0.

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

We can solve this without actually doing the math. Let's look at 64 vs 52. 64 is clearly bigger. Now let's look at 32 vs 42. 32 is clearly smaller. Then, bigger – smaller is greater than smaller – bigger, so Quantity A is bigger.

The first thing to note is the relationship between (–b) and (1 – b):

(–b) < (1 – b) because (–b) + 1 = (1 – b).

Now when b > 1, (1 – b) < 0 and –b < 0. Therefore (–b) < (1 – b) < 0.

Raising a negative number to an odd power produces another negative number.

Thus (–b)a < (1 – b)a < 0.

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

We can solve this without actually doing the math. Let's look at 64 vs 52. 64 is clearly bigger. Now let's look at 32 vs 42. 32 is clearly smaller. Then, bigger – smaller is greater than smaller – bigger, so Quantity A is bigger.

The first thing to note is the relationship between (–b) and (1 – b):

(–b) < (1 – b) because (–b) + 1 = (1 – b).

Now when b > 1, (1 – b) < 0 and –b < 0. Therefore (–b) < (1 – b) < 0.

Raising a negative number to an odd power produces another negative number.

Thus (–b)a < (1 – b)a < 0.

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