Question

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

Answer 1

The expression is:

$\sqrt{\frac{x^{3}x^{8}}{x^{6}}}$

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:

$\sqrt{\frac{x^{11}}{x^{6}}}$

Step 2:

Use division property of exponents:

$\frac{x^{a}}{x^{b}}=x^{a-b}$

$\frac{x^{11}}{x^{6}}=x^{11-6}$

$\frac{x^{11}}{x^{6}}=x^{5}$

This simplifies the expression:

$\sqrt{x^{5}}$

Step 3:

Writing the square root as power 1/2:

$\sqrt{x^{5}}=x^{5*\frac{1}{2} }$

$\sqrt{x^{5}}=x^{\frac{5}{2} }$

Answer:

The final simplified form in x^n form is :

$x^{\frac{5}{2} }$