Question

Express square root of 169x^5 using rational exponents

Answer 1

Remember the following notation:

$a^{n/m}=^n\sqrt[]{a^m}$

Then:

$\sqrt[]{169x^5}=(169x^5)^{1/2}$

Use the following property to simplify the expression:

$(a\cdot b)^n=a^n\cdot b^n$

Then:

$\begin{gathered} (169x^5)^{1/2}=169^{1/2}\cdot(x^5)^{1/2} \\ =13x^{5/2} \end{gathered}$

Therefore, the square root of 169x^5 is:

$13x^{5/2}$