Chapter 10: Q15. (page 528)

Simplify the expression $81^{\sqrt{2}} \div 3^{\sqrt{2}}$ .

Short Answer

Expert verified

The simplified value of expression is $27^{\sqrt{2}}$ .

Step by step solution

Step 1. Write down the given expression.

The given expression is $81^{\sqrt{2}} \div 3^{\sqrt{2}}$ .

Step 2. Simplify the expression.

The given expression $81^{\sqrt{2}} \div 3^{\sqrt{2}}$ is simplified as:

$\begin{array}{l} 81^{\sqrt{2}} \div 3^{\sqrt{2}} = \frac{{(81)}^{\sqrt{2}}}{{(3)}^{\sqrt{2}}} \\ = \frac{{(3^{4})}^{\sqrt{2}}}{{(3)}^{\sqrt{2}}} \\ = \frac{{(3)}^{4 \sqrt{2}}}{{(3)}^{\sqrt{2}}} \\ = 3^{3 \sqrt{2}} \\ = 27^{\sqrt{2}} \end{array}$

Step 3. Conclusion.

The simplified value of expression is $27^{\sqrt{2}}$ .

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Simplify the expression $81^{\sqrt{2}} \div 3^{\sqrt{2}}$ .

Short Answer

Step by step solution

Step 1. Write down the given expression.

Step 2. Simplify the expression.

Step 3. Conclusion.

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Short Answer

Step by step solution

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Step 3. Conclusion.

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Simplify the expression $81^{\sqrt{2}} \div 3^{\sqrt{2}}$ .