Question

(02.01, 02.02 HC)Vanessa and William are stuck simplifying radical expressions. Vanessa has to simplifyx3William has to simplify 15xx.x4. Usingx6full sentences, describe how to fully simplify Vanessa and William's expressions. Describe if Vanessa and William started with equivalentexpressions or if they started with expressions that are not

Answer 1

ANSWER:

$\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=x^{\frac{1}{2}} \end{gathered}$

STEP-BY-STEP EXPLANATION:

We have that the given expression is the following:

$\frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}$

The other expression is the following:

$\sqrt[16]{x\cdot \:x^3\cdot \:x^4}$

We simplify in each case:

$\begin{gathered} \text{ The Vanness expression is simplified by subtracting the exponents, and we obtain the following:} \\ \\ \frac{x^{\frac{4}{3}}}{x^{\frac{5}{6}}}=x^{\frac{4}{3}-\frac{5}{6}}=x^{\frac{1}{2}} \\ \\ \text{ The Williams expression is simplified by adding the exponents, and we obtain the following:} \\ \\ \sqrt[16]{x\cdot\:x^3\cdot\:x^4}=\sqrt[16]{x^{1+3+4}}=\sqrt[16]{x^8}=x^{\frac{8}{16}}=x^{\frac{1}{2}} \end{gathered}$

This means that the expressions are equal