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

Answer:

$a^{-n}$ is $(\frac{1}{a})^{n}$ OR $\frac{1}{a^{n} }$

$a^{0}$ = 1, where a ≠ 0

Step-by-step 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, $2^{-3}=(\frac{1}{2})^{3}$

• You can write it $\frac{1}{2^{3}}$, 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 $(\frac{1}{a})^{n}$ OR $\frac{1}{a^{n} }$

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