Rewrite ^ksqrt(x^p) using rational expressions. Please show all your work and steps on how you got the answer.
To rewrite ^ksqrt(x^p) using rational expressions, we first need to understand what the caret symbol (^) and the sqrt symbol (√) represent.
The caret symbol (^) represents exponentiation, or raising a number to a power. For example, x^p means x raised to the power of p.
The sqrt symbol (√) represents the square root operation, which is the inverse of squaring a number. For example, √x means the square root of x.
Now, let's rewrite ^ksqrt(x^p) using rational expressions.
The square root of x^p, denoted √(x^p), can be rewritten as (x^p)^(1/2) using the exponentiation property of square roots.
Next, we can raise (x^p)^(1/2) to the power of k, denoted [(x^p)^(1/2)]^k. Using the property of exponentiation, this can be simplified to (x^p)^(k/2), since raising a power to another power means multiplying the exponents.
Finally, let's represent (x^p)^(k/2) using a rational expression.
Recall that (x^p) represents x raised to the power of p, denoted x^p. We can raise x^p to the power of k/2 by multiplying the exponents, resulting in x^(pk/2).
Therefore, ^ksqrt(x^p) can be rewritten as x^(pk/2) using rational expressions.
Final expression: x^(pk/2)