Question

Simplify each exponential expression to the form x^n where n is positive.

Answer 1

The expression is:

`\sqrt{(x^(3)x^(8))/(x^(6))}`

We will use following steps to simplify it:

Step 1:

Use product property of exponents:

`x^(a)*x^(b)=x^(a+b)`

`x^(3)*x^(8)=x^(8+3)`

`x^(3)*x^(8)=x^(11)`

That gives us the expression:

`\sqrt{(x^(11))/(x^(6))}`

Step 2:

Use division property of exponents:

`(x^(a))/(x^(b))=x^(a-b)`

`(x^(11))/(x^(6))=x^(11-6)`

`(x^(11))/(x^(6))=x^(5)`

This simplifies the expression:

`\sqrt{x^(5)}`

Step 3:

Writing the square root as power 1/2:

`\sqrt{x^(5)}=x^{5*(1)/(2) }`

`\sqrt{x^(5)}=x^{(5)/(2) }`

Answer:

The final simplified form in x^n form is :

`x^{(5)/(2) }`