Question

K⁽¹/²⁾ * 1/k * (1/k)⁽¹/²⁾:

(a) Simplify the expression.
(b) Identify the equivalent expression with positive exponents.
(c) Determine the value of the expression for a specific value of k.
(d) Express the result as a single radical.

Answer 1

In order to simplify the expression k^(1/2) * 1/k * (1/k)^(1/2), apply the rules of exponents and cancel out common factors to simplify the expression. The equivalent expression with positive exponents is 1/√k. The value of the expression depends on the value assigned to k and can be expressed as 1/√k.

Step-by-step explanation:

In order to simplify the expression k(1/2) * 1/k * (1/k)(1/2), we can apply the rules of exponents.

1. First, simplify the expression within the parentheses (1/k)(1/2) by raising the numerator and denominator to the power of 1/2 separately.
2. Next, simplify the expression k(1/2) * 1/k by multiplying the numerators and the denominators.
3. Finally, simplify the expression by canceling out common factors.

The equivalent expression with positive exponents is 1/√k.

The value of the expression for a specific value of k depends on the value assigned to k. For example, if k = 9, then the expression becomes 1/√9 = 1/3.

The result can be expressed as a single radical by writing it as 1/√k.