Question

DESCRIBE how a power with a zero exponent (a^0) and a power with a negative exponent (a^−n) can be simplified.

Answer 1

`a^(-n)` is
`((1)/(a))^(n)` OR
`(1)/(a^(n) )`

`a^(0)` = 1, where a ≠ 0

Explanation:

To simplify the exponents, you must put it in positive value

Example:

The simplest form of
`2^(-3)` is to change the exponent from negative value to positive value.

• You can do that by reciprocal the number,
  `2^(-3)=((1)/(2))^(3)`

• You can write it
  `(1)/(2^(3))`, because 1 to any power equal 1

That means if you want to simplify
`a^(-n)`, reciprocal a and change the sign of the power from -n to n

The simplest form of
`a^(-n)` is
`((1)/(a))^(n)` OR
`(1)/(a^(n) )`

For any number, a (a ≠ 0), 1 × a = a, so, the reason that any number to the zero power is 1 because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, (1)

Example:

The value of
`(5)^(0)` = 1, because it is the product of no numbers, so it is equal to the multiplicative identity (1)

That means
`a^(0)` = 1, where a ≠ 0

Very important note:

`(0)^(0)` is undefined value