Home > Pre-Algebra > Exponents > Converting Exponents

## Converting Exponents

#### Introduction

Converting exponents to expanded form is simply writing the exponent out in full form. Converting expanded form to exponent means we need to determine the base and exponent and write it in the form: $base^{exponent}$. Converting exponents to words is to write the exponent out in words.

#### Terms

**Exponent**- The number of times to multiply the base.

**Base**- The number being multiplied.

**Cubed**- Any number with an exponent of 3 is said to be cubed.

**Squared**- Any number with an exponent of 2 is said to be squared.

## Lesson

If we are given $2^3$, the expanded form is 2 * 2 * 2 (this is the base multiplied by itself, the exponent number of times). If we are given 2 * 2 * 2 * 2, the exponent form would be base exponent, so in this case the base is 2, and the exponent is 4. Therefore the answer is $2^4$. In words, the same $2^4$ would be written as ‘2 to the power of 4’ or ‘2 to the fourth power’.

*Note:* Any number to the power of 2 or 3 is said to be ‘squared’ or ‘cubed’ respectively.

## Examples

#### Converting Exponent Form to Expanded Form (Example #1)

$x^{3}$

The base x is multiplied 3 times

#### Converting Exponent Form to Expanded Form (Example #2)

$p^{4}$

The base p is multiplied 4 times

#### Converting Expanded Form to Exponent (Example #3)

$\text{y} * \text{x} * \text{x} * \text{x} * \text{y}$

The base x is multiplied 3 times

The base y is multiplied 2 times

#### Converting Expanded Form to Exponent (Example #4)

$\text{p} * \text{p} * \text{x} * \text{x} * \text{x} * \text{a} * \text{a} * \text{p} * \text{p}$

The base x is multiplied 3 times

The base p is multiplied 4 times

The base a is multiplied 2 times

#### Converting Exponent to Words (Example #1)

$2^{3}$

#### Converting Exponent to Words (Example #2)

$x^{3}$

#### Converting Exponent to Words (Example #3)

$5^{6}$

#### Converting Exponent to Words (Example #4)

$z^{9}$