The expression is:
[tex]\sqrt{\frac{x^{3}x^{8}}{x^{6}}}[/tex]
We will use following steps to simplify it:
Step 1:
Use product property of exponents:
[tex]x^{a}*x^{b}=x^{a+b}[/tex]
[tex]x^{3}*x^{8}=x^{8+3}[/tex]
[tex]x^{3}*x^{8}=x^{11}[/tex]
That gives us the expression:
[tex]\sqrt{\frac{x^{11}}{x^{6}}}[/tex]
Step 2:
Use division property of exponents:
[tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]
[tex]\frac{x^{11}}{x^{6}}=x^{11-6}[/tex]
[tex]\frac{x^{11}}{x^{6}}=x^{5}[/tex]
This simplifies the expression:
[tex]\sqrt{x^{5}}[/tex]
Step 3:
Writing the square root as power 1/2:
[tex]\sqrt{x^{5}}=x^{5*\frac{1}{2} }[/tex]
[tex]\sqrt{x^{5}}=x^{\frac{5}{2} }[/tex]
Answer:
The final simplified form in x^n form is :
[tex]x^{\frac{5}{2} }[/tex]
