ewrite in simplest radical form 1/x^-3/6. Show each step of your process.

To simplify the expression \( \frac{1}{x^{-3}} \div 6 \) and express it in simplest radical form, let's go step by step.

### Step 1: Simplify the expression inside the fraction.
The expression is \( \frac{1}{x^{-3}} \).

- Recall that \( x^{-n} = \frac{1}{x^n} \).
- Therefore, \( \frac{1}{x^{-3}} \) is equivalent to \( x^3 \).

Now, the expression becomes:

\[
x^3 \div 6
\]

### Step 2: Express the division as a fraction.
The expression \( x^3 \div 6 \) can be written as:

\[
\frac{x^3}{6}
\]

### Step 3: Check if further simplification is possible.
At this point, \( \frac{x^3}{6} \) is already in its simplest form. There are no further factors to simplify.

Since no radical terms were introduced or needed, the final expression in simplest radical form remains:

\[
\boxed{\frac{x^3}{6}}
\]

Would you like more details or have any questions?

### Related Questions:
1. How do you simplify expressions with negative exponents?
2. What is the rule for dividing powers with the same base?
3. How do you express a fractional exponent in radical form?
4. Can you explain how to simplify \( \frac{x^{-2}}{x^{-3}} \)?
5. What does it mean to rationalize the denominator of a fraction?
6. How do you simplify \( \frac{1}{\sqrt{x}} \) divided by a constant?
7. What is the difference between \( \frac{1}{x^{-2}} \) and \( x^2 \)?
8. How do you simplify expressions with exponents and fractions?

### Tip:
When simplifying expressions with exponents, always handle the exponent rules first before simplifying the rest of the expression.

Learn how to simplify the expression \( \frac{1}{x^{-3}} \div 6 \) step-by-step to its simplest radical form. This problem covers exponents and simplification of expressions, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation