# Power (Exponent)

How to solve the power (exponent) of a number: definition, examples, and their solutions.

## Definition

*a*^{m} means

multiplying *a* *m* times.*a*: Base*m*: Exponent

How to read *a*^{m}:*a* to the *m**a* to the *m*th*a* to the power of *m**a* to the power of *m*th*a* raised to the *m*th power

## Example 1

When the exponent is 2,

then it's read as [squared].

So 3^{2} is read as [3 squared].

3^{2} means

multiplying 3 2 times.

So 3⋅3 = 9.

## Example 2

When the exponent is 3,

then it's read as [cubed].

So 2^{3} is read as [2 cubed].

2^{3} means

multiplying 2 3 times.

Multiply the first pair numbers.

Then 2⋅2⋅2 = 4⋅2.

Then 4⋅2 = 8.

## Example 3

(-1)^{4} means

multiplying (-1) 4 times.

(-1)⋅(-1) = +1

So (-1)⋅(-1)⋅(-1)⋅(-1)

= (+1)⋅(+1).

So (+1)⋅(+1) = 1.

As you can see,

if the base is (-)

and if the exponent is even,

then the number is (+).

This is because

the product of each pair of (-) numbers becomes (+):

(-)⋅(-) = (+).

## Example 4

(-2)^{5} means

multiplying (-2) 5 times.

(-2)⋅(-2) = +4

So (-2)⋅(-2)⋅(-2)⋅(-2)⋅(-2)

= 4⋅4⋅(-2).

4⋅4 = 16

So 4⋅4⋅(-2) = 16⋅(-2).

So 16⋅(-2) = -32.

As you can see,

if the base is (-)

and if the exponent is odd,

then the number is (-).

This is because

the product of each pair of (-) numbers becomes (+):

(-)⋅(-) = (+),

and the remaining one (-)

makes the sign of the number (-).