Chapter 11, Problem 1RE

To determine

Whether the statement “$2x^0=1$” is true or false.

Answer to Problem 1RE

The given statement is $\underset{\_}{\text{false}}$.

Explanation of Solution

Rule used:

The exponent rule: $a^0=1\text{ where }a\ne 0$.

Calculation:

Given that, the equation is $2x^0=1$.

Consider the expression $2x^0$.

Use exponent rule and simplify the expression as follows.

$\begin{array}{c}2x^0=2\left(1\right)\left(\because x^0=1\right)\\ =2\end{array}$

The value of the expression is $2$. But, the given statement $2x^0=1$.

Therefore, the given statement “$2x^0=1$” is $\underset{\_}{\text{false}}$.