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Vilka [71]
4 years ago
7

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

Mathematics
1 answer:
vaieri [72.5K]4 years ago
4 0

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} }


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