How do you simplify 81^sqrt2 div 3^sqrt2?

1 Answer

${3}^{3 \sqrt{2}} = {27}^{\sqrt{2}}$

Explanation:

We can take our original:

${81}^{\sqrt{2}} \div {3}^{\sqrt{2}}$

and rewrite it this way:

${\left({3}^{4}\right)}^{\sqrt{2}} / {3}^{\sqrt{2}}$

which can then be written as:

$\frac{{3}^{4 \sqrt{2}}}{{3}^{\sqrt{2}}}$

and then we can write it as:

$\frac{{3}^{3 \sqrt{2} + \sqrt{2}}}{{3}^{\sqrt{2}}} = \frac{{3}^{3 \sqrt{2}} \times {3}^{\sqrt{2}}}{{3}^{\sqrt{2}}}$

cancel the two like terms and get:

$\frac{{3}^{3 \sqrt{2}} \times \cancel{{3}^{\sqrt{2}}}}{\cancel{{3}^{\sqrt{2}}}} = {3}^{3 \sqrt{2}} = {27}^{\sqrt{2}}$