### All GMAT Math Resources

## Example Questions

### Example Question #1 : Powers & Roots Of Numbers

Solve:

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**Correct answer:**

Solve

### Example Question #1 : Understanding Powers And Roots

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**Correct answer:**

### Example Question #3 : Powers & Roots Of Numbers

Solve:

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**Correct answer:**

First, FOIL:

Factor out

### Example Question #2 : Understanding Powers And Roots

Solve:

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**Correct answer:**

First factor.

Simplify.

### Example Question #5 : Powers & Roots Of Numbers

If , what is

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**Correct answer:**

### Example Question #6 : Powers & Roots Of Numbers

Evaluate:

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### Example Question #1 : Powers & Roots Of Numbers

Simplify this expression as much as possible:

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The expression cannot be simplified further

**Correct answer:**

### Example Question #1 : Understanding Powers And Roots

If the side length of a cube is tripled, how does the volume of the cube change?

**Possible Answers:**

Not enough informatin is given.

Volume becomes 9 times larger.

The volume doesn't change.

Volume becomes 27 times larger.

Volume becomes 3 times larger.

**Correct answer:**

Volume becomes 27 times larger.

The equation for the volume of a cube is . If the length is tripled, it becomes , and , so the volume increases by 27 times the original size.

### Example Question #3 : Understanding Powers And Roots

Simplify

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**Correct answer:**

This can either be done by brute force (slow) or by recognizing the properties of roots and exponents (fast). Roots are simply fractional exponents: , , etc. so they can be done in any order.

So we see a cube root, we can immediately cancel that with the exponent of 3. taking us from here: to . We now simplify to get

### Example Question #1 : Powers & Roots Of Numbers

In the sequence 1, 3, 9, 27, 81, … , each term after the first is three times the previous term. What is the sum of the 9th and 10th terms in the sequence?

**Possible Answers:**

**Correct answer:**

We can rewrite the sequence as , , , , , … ,

and we can see that the 9th term in the sequence is and the 10th term in the sequence is . Therefore, the sum of the 9th and 10th terms would be

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