# GMAT Math : Powers & Roots of Numbers

## Example Questions

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Solve:

Explanation:

Solve

Explanation:

Solve:

Explanation:

First, FOIL:

Factor out

Solve:

Explanation:

First factor.

Simplify.

If , what is

Explanation:

Evaluate:

Explanation:

### Example Question #1581 : Problem Solving Questions

Simplify this expression as much as possible:

The expression cannot be simplified further

Explanation:

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

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

The volume doesn't change.

Volume becomes 27 times larger.

Volume becomes 9 times larger.

Volume becomes 3 times larger.

Not enough informatin is given.

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 #1581 : Gmat Quantitative Reasoning

Simplify

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 #2 : 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?