Bevan Mcdonald

2021-01-08

Radicals and Exponents Evaluate each expression:
a) $\frac{\sqrt{132}}{\sqrt{3}}$
b) $\sqrt[3]{2}\sqrt[3]{32}$
c) $\sqrt[4]{\frac{1}{4}}\sqrt[4]{\frac{1}{64}}$

StrycharzT

a) Formula used:
Power of nth roots:
$\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{a}}$
Where n is any positive integer and a and b are bases.
Calculation:
The given exponential expression is $\frac{\sqrt{132}}{\sqrt{3}}$
Use the above-mentioned formula and calculate the value of $\frac{\sqrt{132}}{\sqrt{3}}$ as shown below.
$\frac{\sqrt{132}}{\sqrt{3}}=\frac{\sqrt{11\cdot 2\cdot 2\cdot 3}}{\sqrt{3}}$
$=\frac{2\sqrt{11}\cdot \sqrt{3}}{\sqrt{3}}$
$=2\sqrt{11}$
Thus, the value of exponential is $2\sqrt{11}$
b) Calculation:
Use the above mentioned formula and simplify the given expression as shown below.
$\sqrt[3]{2}\sqrt[3]{32}=\sqrt[3]{2}\sqrt[3]{2\cdot 2\cdot 2\cdot 2\cdot 2}$
$={\left({2}^{6}\right)}^{\frac{1}{3}}$
$={2}^{2}$
$=4$
Thus, the value of exponential expression is 4.
c) Calculation:
$\sqrt[4]{\frac{1}{4}}\sqrt[4]{\frac{1}{64}}=\sqrt[4]{\frac{1}{4}}\sqrt[4]{\frac{1}{4·4·4}}$
$=\sqrt[4]{\frac{1}{{\left(4\right)}^{4}}}$
$=\frac{1}{{\left({4}^{4}\right)}^{\frac{1}{4}}}$
$=\frac{1}{4}$
The value of exponential is $\frac{1}{4}.$

Jeffrey Jordon