To determine the value of the expression [tex]\((2x)^0\)[/tex] where [tex]\( x \neq 0 \)[/tex], let's proceed with a detailed step-by-step solution:
1. Understanding the Expression:
- The given expression is [tex]\((2x)^0\)[/tex].
- The base of the expression is [tex]\(2x\)[/tex], and the exponent is [tex]\(0\)[/tex].
2. Exponential Rule:
- According to the laws of exponents, any non-zero number raised to the power of [tex]\(0\)[/tex] is equal to [tex]\(1\)[/tex]. Mathematically, [tex]\( a^0 = 1 \)[/tex] for any [tex]\( a \neq 0 \)[/tex].
3. Application of the Rule:
- Here, [tex]\(2x\)[/tex] represents the base, and it is a non-zero value since [tex]\(x \neq 0\)[/tex].
- Therefore, applying the exponent rule: [tex]\((2x)^0 = 1\)[/tex].
So, the value of [tex]\((2x)^0\)[/tex] is:
[tex]\[
1
\][/tex]
Hence, [tex]\((2x)^0 = 1\)[/tex] when [tex]\(x \neq 0\)[/tex].
