express 1/ 2x in the form ax^b, where a and b are rational constants

The expression \( \frac{1}{2x} \) can be rewritten in the form \( ax^b \), where \( a \) and \( b \) are rational constants.

\[
\frac{1}{2x} = \frac{1}{2} \cdot \frac{1}{x}
\]
Using the property \( \frac{1}{x} = x^{-1} \), we have:
\[
\frac{1}{2x} = \frac{1}{2} \cdot x^{-1}
\]
Thus, the expression in the form \( ax^b \) is:
\[
\frac{1}{2x} = \frac{1}{2}x^{-1}
\]
where \( a = \frac{1}{2} \) and \( b = -1 \).

Would you like more details or have any further questions?

Here are 5 related questions to expand on this topic:
1. How would you express \( \frac{1}{3x^2} \) in the form \( ax^b \)?
2. What is the general form of \( \frac{1}{kx^n} \) where \( k \) and \( n \) are constants?
3. How can you simplify expressions like \( \frac{1}{x^3} \)?
4. How does \( \frac{1}{x} \) relate to powers of \( x \)?
5. What is the inverse of \( x^{-1} \) in terms of powers of \( x \)?

**Tip:** When simplifying fractions with variables, remember to apply negative exponents for terms in the denominator.

Express 1/2x in the form ax^b, where a and b are rational constants.

Learn how to express 1/2x in the form ax^b with detailed steps, covering concepts like negative exponents and algebraic manipulation. This problem involves understanding the expression of variables using the laws of exponents. Suitable for Grades 9-11.

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