# GMAT Math : Understanding powers and roots

## Example Questions

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

Solve:

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Correct answer:

Explanation:

Solve

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

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

Solve:

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Correct answer:

Explanation:

First, FOIL:

Factor out

### Example Question #4 : Understanding Powers And Roots

Solve:

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Correct answer:

Explanation:

First factor.

Simplify.

### Example Question #5 : Understanding Powers And Roots

If , what is

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Correct answer:

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### Example Question #6 : Understanding Powers And Roots

Evaluate:

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Correct answer:

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### Example Question #7 : Understanding Powers And Roots

Simplify this expression as much as possible:

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The expression cannot be simplified further

Correct answer:

Explanation:

### Example Question #8 : 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.

Volume becomes 27 times larger.

Volume becomes 3 times larger.

The volume doesn't change.

Correct answer:

Volume becomes 27 times larger.

Explanation:

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 #9 : Understanding Powers And Roots

Simplify

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Correct answer:

Explanation:

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 #10 : Understanding Powers And Roots

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:

Explanation:

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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