simplify 1/2 times x to the power of negative half

To simplify \( \frac{1}{2} \times x^{-\frac{1}{2}} \), follow these steps:

1. Multiply the constants first: \( \frac{1}{2} \) stays the same.
2. Combine the powers of \( x \), using the rule \( a \cdot b^n = a \cdot b^n \), since there are no like terms to combine.

Thus, the expression simplifies to:
\[
\frac{1}{2}x^{-\frac{1}{2}}
\]

Since \( x^{-\frac{1}{2}} \) is the same as \( \frac{1}{\sqrt{x}} \), the expression can also be written as:

\[
\frac{1}{2\sqrt{x}}
\]

This is the simplified form.

Would you like any further details or have any questions?

Here are 5 related questions to explore further:
1. What is the general rule for multiplying exponents?
2. How do you simplify an expression with multiple negative exponents?
3. Can you convert any expression with a negative exponent to fractional form?
4. What happens if the exponent is positive instead of negative?
5. How do you differentiate or integrate a function with fractional exponents?

**Tip:** When dealing with negative exponents, remember that they represent the reciprocal of the base raised to the positive exponent.

Learn how to simplify the expression 1/2 times x to the power of -1/2 with a step-by-step explanation. This solution covers key algebraic concepts like exponents and negative exponent rules. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation