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)`