Ava-May Nelson

2021-02-11

To determine:
To calculate:
a) The indicated operation $\sqrt{4}\left\{cd\right\}\cdot \sqrt{5}\left\{{c}^{2}\right\}$
b) The indicated operation $\sqrt{4}\left\{y\sqrt{3}\left\{y\right\}\right\}$
c) The indicated operation $\sqrt{5}\left\{x\right\}+\sqrt{5}\left\{y\right\}+\sqrt{4}\left\{x\right\}$

SoosteethicU

Step 1 a) Formula Given:
Consider the given expression $\sqrt{4}\left\{cd\right\}\cdot \sqrt{5}\left\{{c}^{2}\right\}$
Rewrite the expression with rational exponents
$\sqrt{4}\left\{cd\right\}\cdot \sqrt{5}\left\{{c}^{2}\right\}$
$=\left(cd\cdot \left(cd\right)\right)$

Combine the like bases and use the property

$=\sqrt{20}\left\{{c}^{13}{d}^{5}\right\}$
Therefore, the value of $\sqrt{4}\left\{cd\right\}\cdot \sqrt{5}\left\{{c}^{2}\right\}$ is $\sqrt{20}\left\{{c}^{13}{d}^{5}\right\}$
Step 2
b) Formula Given: ${\left({a}^{m}\right)}^{n}={a}^{mn}$

Consider the given expression $\sqrt{4}\left\{y\sqrt{3}\left\{y\right\}\right\}$
Rewrite the expression with rational exponents
$\sqrt{4}\left\{y\sqrt{3}\left\{y\right\}\right\}$
$=\left({}_{\left\{.\right\}}^{y}$
Use the property to get,
$={\left({y}^{\frac{4}{3}}\right)}^{\frac{1}{4}}$
Use the property ${\left({a}^{m}\right)}^{n}={a}^{mn}$ to get,
$={y}^{\frac{1}{3}}$
$=\sqrt{3}\left\{y\right\}$
Therefore, the value of $\sqrt{4}\left\{y\sqrt{3}\left\{y\right\}\right\}$ is $\sqrt{3}\left\{y\right\}$
Step 3

c) Consider the given expression $\sqrt{5}\left\{x\right\}+\sqrt{5}\left\{y\right\}+\sqrt{4}\left\{x\right\}$
Therefore, the value of $\sqrt{5}\left\{x\right\}+\sqrt{5}\left\{y\right\}+\sqrt{4}\left\{x\right\}$ is