Powers is another way to write a product.

a * a * a * a = a^{4}

Power with integer exponent is

a^{m}

Here a is a real number, and m is an integer.

The expression

a^{m}

is called a power with integer exponent.

The number a called the base

the base –> a^{m}

The number m is called the exponent

a^{m <– the exponent}

We say "a to the m-th power".

It is important that

1. The exponent is an integer

2. The base number can be any real number.

2. The base number can be any real number.

The power with integer exponent a^{m} is equal to the product of a multiplied by itself m times:

a^{m} = a * a * a * ... (m times)

Powers with integer exponents can be defined as:

1. a^{m} = a * a * a * ... (m times, here m is a natural number)

2. a^{0} = 1

3. a^{-m} = 1/a^{m}

2. a

3. a

Here a is a real number, a ≠ 0, and m is an integer.

Examples of powers with integer exponents.

5^{4} = 5 * 5 * 5 * 5 = 625

6^{3} = 6 * 6 * 6 = 216

6

Examples. The exponent is equal to 0.

5^{0} = 1

(-6)^{0} = 1

(-6)

Examples of powers with negative exponents.

5^{-2} = 1/5^{2} = 1/25

(-6)^{-2} = 1/(-6)^{2} = 1/36

(-6)