Power (Exponent)

Power (Exponent)

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

Definition

a^m means multiplying a m times.

am means
multiplying a m times.

a: Base
m: Exponent

How to read am:

a to the m
a to the mth

a to the power of m
a to the power of mth

a raised to the mth power

Example 1

Simplify the given expression. 3^2

When the exponent is 2,
then it's read as [squared].

So 32 is read as [3 squared].

32 means
multiplying 3 2 times.

So 3⋅3 = 9.

Example 2

Simplify the given expression. 2^3

When the exponent is 3,
then it's read as [cubed].

So 23 is read as [2 cubed].

23 means
multiplying 2 3 times.

Multiply the first pair numbers.

Then 2⋅2⋅2 = 4⋅2.

Then 4⋅2 = 8.

Example 3

Simplify the given expression. (-1)^4

(-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

Simplify the given expression. (-2)^5

(-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 (-).