1Cademy - Simplifying $$(2x)^0$$ Using the Zero Exponent

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Zero Exponent

Example

Simplifying $(2x)^0$ Using the Zero Exponent

Simplify $(2x)^0$ by applying the Product to a Power Property followed by the Zero Exponent rule.

Start with the expression $(2x)^0$ . Apply the Product to a Power Property to distribute the exponent to each factor inside the parentheses:

$(2x)^0 = 2^0 \cdot x^0$

Now apply the Zero Exponent rule to each factor separately. Since $2 \neq 0$ and $x \neq 0$ :

$2^0 \cdot x^0 = 1 \cdot 1 = 1$

This confirms that any nonzero expression — not just a single number or variable — raised to the zero power equals $1$ . Whether the base is a product like $2x$ , a single variable, or a whole number, the result is always $1$ as long as the base is nonzero.