### Let's Think About It

Horatio is a carpenter building a habitat for tigers at his local zoo. He has been told that the tiger’s enclosure needs to be at least 1720 cubic feet. Horatio has only ever built two animal habitats before, and he was hoping to use one of those as a model. One habitat was

cubic feet, and the other was cubic feet. Which of Horatio’s previous habitat designs meets the requirements for the tiger habitat?In this concept, you will learn how powers, bases, and exponents work together.

### Guidance

An **exponent** is a little number that shows how many times to multiply a certain number by itself.

Let's look at an example:

The large number, 4, is called the **base**.

The small number, 2, is called the **exponent**. This number tells you how many times to multiply the base by itself.

When a base has an exponent of 2, such as

When a base has an exponent of 3, such as

For all other exponents, you read the exponent as a **power**. For example,

** 35 **is read as "three to the fifth power".

An exponent tells you how many times the base should be multiplied by itself. If you look at a number with an exponent written out the long way, you can see why exponents are useful.

In this case, there are three factors of 7. Remember that factors are numbers or variables multiplied by each other.

In this case, there are ten factors of 5.

Exponents are a multiplication shortcut a lot like the way that multiplication is an addition shortcut.

### Guided Practice

Write out the factors of

Once you have written out all the factors, simply multiply from left to right.

The answer is 243.

### Examples

#### Example 1

Write

First, identify the base number, which is the big number that will be multiplied by itself. In this case, the base is 6.

Next, consider the power, which is the small number that describes how many times the number will be multiplied. In this case, the power is 3, so the base will be multiplied by itself 3 times.

The solution is "6 times 6 times 6."

#### Example 2

Write out the factors of

First, remember that factors are numbers that are multiplied by each other to equal a certain value.

Next, identify the base number, which is the big number that will be multiplied by itself. In this case, the base is 4.

Then consider the power, which is the small number that describes how many times the number will be multiplied. In this case the power is 5, so the base will be multiplied by itself 5 times.

The solution is

#### Example 3

Which is the base number:

First, remember that the base is the big number that is multiplied by itself.

Then, remember that the power is the little number that describes how many times to multiply the base by itself.

The answer is that the base in the expression

### Follow Up

Remember Horatio and his tiger housing project?

Horatio needs to figure out which dimensions are closest to 1720 cubic feet: 9^{3} cubic feet or 12^{3} cubic feet.

First, write out the factors for each expression.

Next, multiply.

The answer is 12^{3}.

Horatio can use his old 12^{3} cubic feet habitat design, which even gives the tigers a little extra room.

### Video Review

### Explore More

Write each power out in words.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Evaluate each expression (they are the same expressions as in problems 1 - 10).

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.