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Simplify. $\newline$ $1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}$ $\newline$ ______

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Multiplication with rational exponents

Full solution

Q. Simplify.

\newline

1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

\newline

______

Multiply Bases with Exponent: Multiply the bases with the same exponent: $1^{1/4} \times 1^{1/4} = (1 \times 1)^{1/4}.$
Simplify Multiplication: Simplify the multiplication of the bases: $(1 \times 1)^{\frac{1}{4}} = 1^{\frac{1}{4}}$ .
Apply Fourth Root Property: Any number to the power of $\frac{1}{4}$ is the fourth root of that number; since $1$ is the identity for multiplication, $1^{\frac{1}{4}} = 1$ .

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