Question
show all the steps it took to get your answer.
rewrite r/sqrt q^t using a rational expression
rewrite r/sqrt q^t using a rational expression
Answers
GPT 3.5
To rewrite $r/\sqrt{q^t}$ as a rational expression, we need to rationalize the denominator.
1. Begin by expressing $\sqrt{q^t}$ as $q^{t/2}$ since $\sqrt{q^t} = q^{t/2}$.
Therefore, $r/\sqrt{q^t}$ becomes $r/q^{t/2}$.
2. Next, rationalize the denominator by multiplying both the numerator and denominator by $q^{t/2}$ to get rid of the square root in the denominator.
This gives us $r*q^{t/2}/(q^{t/2})^2$.
3. Simplify the expression by combining the exponents in the denominator.
The expression now becomes $r*q^{t/2}/q^t$.
4. Finally, simplify further by subtracting the exponents in the denominator and combine terms.
The final answer is $\boxed{r/q^{t/2}}$.
1. Begin by expressing $\sqrt{q^t}$ as $q^{t/2}$ since $\sqrt{q^t} = q^{t/2}$.
Therefore, $r/\sqrt{q^t}$ becomes $r/q^{t/2}$.
2. Next, rationalize the denominator by multiplying both the numerator and denominator by $q^{t/2}$ to get rid of the square root in the denominator.
This gives us $r*q^{t/2}/(q^{t/2})^2$.
3. Simplify the expression by combining the exponents in the denominator.
The expression now becomes $r*q^{t/2}/q^t$.
4. Finally, simplify further by subtracting the exponents in the denominator and combine terms.
The final answer is $\boxed{r/q^{t/2}}$.