Questions: (a) 1^(1/4)= (b) -216^(1/3)=

Transcript text: (a) \[ 1^{\frac{1}{4}}= \] $\square$ (b) \[ -216^{\frac{1}{3}}= \] $\square$

Solution

Solution Approach

(a) To find $1^{\frac{1}{4}}$, we need to calculate the fourth root of 1. Any number raised to any power of 1 is always 1.

(b) To find $-216^{\frac{1}{3}}$, we need to calculate the cube root of -216. The cube root of a negative number is also negative.

Step 1: Calculate $1^{\frac{1}{4}}$

To find $1^{\frac{1}{4}}$, we evaluate the fourth root of 1: \[ 1^{\frac{1}{4}} = 1 \]

Step 2: Calculate $-216^{\frac{1}{3}}$

Next, we calculate the cube root of $-216$: \[ -216^{\frac{1}{3}} = -6 \] This is because $(-6)^3 = -216$.

The results are:

Thus, the final answers are: \[ \boxed{1} \quad \text{and} \quad \boxed{-6} \]

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