EunoR

2020-10-20

To simplify:
The given expression $\left(2\sqrt{a}\right)\left(\sqrt{3}\left\{{a}^{2}\right\}\right)$

dessinemoie

Step 1
Law of exponents:
For any rational exponent $\frac{m}{n}$ in lowest terms, where m and n are integers and $n>0,$ we define
${a}^{\frac{m}{n}}={\left(\sqrt{n}\left\{a\right\}\right)}^{m}=\sqrt{n}\left\{{a}^{m}\right\}$
If n is even, then we require that $a\ge 0$
Step 2
Consider the given expression,
$\left(2\sqrt{a}\right)\left(\sqrt{3}\left\{{a}^{2}\right\}\right)$
By using the law of exponents,
$\left(2\sqrt{a}\right)\left\{\sqrt{3}\left\{{a}^{2}\right\}\right)=\left(2{a}^{\frac{1}{2}}\right)\left({a}^{\frac{2}{3}}\right)$

Applying the exponent rule: we get
$=2{a}^{\frac{1}{2}+\frac{2}{3}}$
$=2{a}^{\frac{7}{6}}$
Final Statement:
The simplified form of $\left(2\sqrt{a}\right)\left(\sqrt{3}\left\{{a}^{2}\right\}\right)$ is $2{a}^{\frac{7}{6}}$

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