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# Exponents

## Raising One Power to Another

When one power is raised to another, we multiply exponents:

This is true for all kinds of exponents, positive and negative (and as we will see later, fractional).

### Examples

Raising a Positive Power to a Positive Power

Long solution:

Short solution:

Have a look at some more worked examples:

 ( ) = = = x x x

### Exercise

Now practice some of the following exercises:

 ( x ) = x

### Examples

Raising a Positve Power to a Negative Power

Long solution:

Short solution:

Study some more worked examples showing the longer solution:

 1 1 ( ) = ( ) = = x x x x

### Exercise

Now practice by solving some of the following exercises. Here you can use the short solution and just enter the final answer:

 ( x ) = x

### Examples

Raising a Negative Power to a Positive Power

Long solution:

Short solution:

Study some more worked examples:

 = = = = = ( ) 1 1 1 1 s ( ) s s s s s

### Exercise

Practice by solving some of the following exercises:

 ( x ) = x

### Example

Finally just one long solution for a negative exponent raised to a negative exponent.

### Exercise

Solve some of these mixed exercises:

 ( m ) = m