Chapter 15.1, Problem 6MRE

To determine

Simplify without negative exponents.

Answer to Problem 6MRE

  $2^{5\sqrt{2}}$

Explanation of Solution

Given information:

Given: $8^{\sqrt{2}}{.2}^{\sqrt{8}}$

Calculation:

Here we have:

  $8^{\sqrt{2}}{.2}^{\sqrt{8}}$

Now, we will write it in its simplest form:

  $\begin{array}{l}{8}^{\sqrt{2}}{.2}^{\sqrt{8}}={\left(2^3\right)}^{\sqrt{2}}{.2}^{\sqrt{4\times 2}}\left[\therefore 8=2^3\right]\\ 8^{\sqrt{2}}{.2}^{\sqrt{8}}=2^{3\sqrt{2}}{.2}^{2\sqrt{2}}\left[\therefore {\left(a^m\right)}^n=a^{m\times n}\right]\\ 8^{\sqrt{2}}{.2}^{\sqrt{8}}=2^{3\sqrt{2}+}{}^{2\sqrt{2}}\\ 8^{\sqrt{2}}{.2}^{\sqrt{8}}=2^{5\sqrt{2}}\end{array}$

Hence, the required answer is $2^{5\sqrt{2}}$ .