DISCUSS MATHEMATICAL THINKING Let x be a nonnegative real number. Determine whether the statement is always, sometimes, or ne true. x^1/3=sqrt [3](x) Always Sometimes Never Justify your answer.

Question

DISCUSS MATHEMATICAL THINKING Let x be a nonnegative real number. Determine whether the statement is always, sometimes, or ne true. x^1/3=sqrt [3](x) Always Sometimes Never Justify your answer.

Answer 1

### Always

Answer 2

## Step 1: Definition of Fractional Exponents### The expression

is defined as the

th root of

, denoted by

, when

is a positive integer. This holds true for non-negative real numbers

.## Step 2: Applying the Definition to the Given Problem### In our case, we have

, which, according to the definition, is equivalent to

.## Step 3: Considering the Domain### The statement holds true for non-negative real numbers. For negative real numbers, the cube root is defined, so the statement also holds true for negative real numbers.

Question

DISCUSS MATHEMATICAL THINKING Let x be a nonnegative real number. Determine whether the statement is always, sometimes, or ne true. x^1/3=sqrt [3](x) Always Sometimes Never Justify your answer.

Solution

Answer

Explanation