Question

simplify.
$1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}$

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \cdot a^n = a^{m+n}$.
$1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}} = 1^{\frac{1}{4}+\frac{1}{4}}$

Step2: Add the exponents

Calculate the sum of the fractions.
$1^{\frac{1}{4}+\frac{1}{4}} = 1^{\frac{2}{4}} = 1^{\frac{1}{2}}$

Step3: Simplify the exponential term

Any non-zero number to the power of $\frac{1}{2}$ is its square root; $\sqrt{1}=1$.
$1^{\frac{1}{2}} = 1$

Answer:

1