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What is the value of [tex](2x)^{\circ}, x \neq 0[/tex]?

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GinnyAnswer
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].
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