Rewrite k(sqrt x^p) using a rational expression. Show all steps
To rewrite k(sqrt(x^p)) using a rational expression, we need to eliminate the square root by rationalizing the denominator.
Step 1: Multiply the expression by a fraction equal to 1, where both the numerator and denominator contain the conjugate of the square root term.
k(sqrt(x^p)) * (sqrt(x^p) / sqrt(x^p))
Step 2: Simplify the numerator and denominator.
(k * sqrt(x^p) * sqrt(x^p)) / (sqrt(x^p) * sqrt(x^p))
= k * (x^p) / (sqrt(x^p) * sqrt(x^p))
Step 3: Simplify the denominator.
= k * (x^p) / (sqrt(x^(p+p)))
Step 4: Simplify the exponent in the denominator.
= k * (x^p) / (sqrt(x^(2p)))
Step 5: Take the square root of the exponent and rewrite the expression.
= k * (x^p) / (x^p)
Finally, cancel out the common terms:
= k.