# GMAT Math : Understanding powers and roots

## Example Questions

← Previous 1 3 4 5

Solve:

Explanation:

Solve

Explanation:

Solve:

Explanation:

First, FOIL:

Factor out

Solve:

Explanation:

First factor.

Simplify.

If , what is

Explanation:

Evaluate:

Explanation:

### Example Question #7 : Powers & Roots Of Numbers

Simplify this expression as much as possible:

The expression cannot be simplified further

Explanation:

### Example Question #8 : Powers & Roots Of Numbers

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

The volume doesn't change.

Not enough informatin is given.

Volume becomes 3 times larger.

Volume becomes 27 times larger.

Volume becomes 9 times larger.

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 : Powers & Roots Of Numbers

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 #10 : 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?