Chapter 12, Problem 16CCSR

To determine

Find the exponential form.

Answer to Problem 16CCSR

  $option\left(b\right)$

  $9n^{\frac{3}{2}}$

Explanation of Solution

Given information:

Given: $\sqrt{81n^3}$

  $\left(a\right)9n^{\frac{1}{2}}\left(b\right)9n^{\frac{3}{2}}\left(c\right)81n^{\frac{3}{2}}\left(d\right)81n^{\frac{1}{2}}$

Calculation:

Here, we have:

  $\sqrt{81n^3}$

Now, we know that any square expression can be written in the form of exponents in fraction as $a^{\frac{1}{2}}$ .

  $\begin{array}{l}\sqrt{81n^3}={\left(81n^3\right)}^{\frac{1}{2}}\\ {\left(81n^3\right)}^{\frac{1}{2}}=\left({81}^{\frac{1}{2}}\right)\left(n^{3\times \frac{1}{2}}\right)\\ {\left(81n^3\right)}^{\frac{1}{2}}={\left(9^2\right)}^{\frac{1}{2}}{n}^{\frac{3}{2}}\\ {\left(81n^3\right)}^{\frac{1}{2}}=9n^{\frac{3}{2}}\end{array}$

Hence, the correct answer is $option\left(b\right)$ .