Question

Evaluate the expression. \(0^{0}\)

Short answer

Hence, the expression \(0^{0}\) is conventionally defined as 1 for computational purposes.

Step-by-step solution

Direct substitution

Directly substituting values, we get \(0^{0}\). This is an indeterminate form, so we will use a convention to interpret its value.

Conventional interpretation

In mathematics, the convention is that \(0^{0} = 1\). This is because one way of interpreting an exponent is as repeated multiplication. In the expression \(0^{0}\), we ideally have zero multiplied to itself zero times. As there is no multiplication actually happening, we use the law of exponents which conventionally uses 1 for any number to the power of 0.