# Radicals and Exponents Evaluate each expression: a) 2 sqrt[3]{81} b) frac{sqrt{18}}{sqrt{25}} c) sqrt{frac{12}{49}}

Radicals and Exponents Evaluate each expression:
a) $2\sqrt{3}\left\{81\right\}$
b) $\frac{\sqrt{18}}{\sqrt{25}}$
c) $\sqrt{\frac{12}{49}}$
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mhalmantus
a) Formula for nth root:
$\sqrt{n}\left\{a\right\}={a}^{\frac{1}{n}}$
Laws of exponents:
${\left({a}^{m}\right)}^{n}={a}^{mn}$
Calculation:
Use the above-mentioned formula and simplify the expression $2\sqrt{3}\left\{81\right\}$ as shown below.
$2\sqrt{3}\left\{81\right\}=2\sqrt{3}\left\{{3}^{4}\right\}$

On further simplification of the above equation, the following is obtained.

$=6\sqrt{3}\left\{3\right\}$
Therefore, the value of expression
b) Use the formula mentioned in part (a) and simplify the expression $\frac{\sqrt{18}}{\sqrt{25}}$ as shown below.

$=\frac{3\sqrt{2}}{5}$
Therefore, the value of expression $\frac{\sqrt{18}}{\sqrt{25}}$ is $\frac{3\sqrt{2}}{5}$
c) Use the formula mentioned in part (a) and simplify the expression as shown below.

$=\frac{2\sqrt{3}}{7}$
Therefore, the value of expression $\sqrt{\frac{12}{49}}$ is $\frac{2\sqrt{3}}{7}.$