Simplify the radical expression 11a264b63

Question

Aniqa O&#039;Neill · Accepted Answer

Simplilfying the given radical expression (involving fractional exponents) means removing roots as much as possible, using the laws of exponents (powers)
First apply the rule
$\sqrt[n]{\frac{x}{y}} = \sqrt[n]{\frac{x}{\sqrt[n]{y}}}$
Here, $x = 11 a^{2}, y = 64 b^{6} = {(4)}^{3} b^{6} = {(4 b^{2})}^{3}$
So,
$\sqrt[3]{\frac{11 a^{2}}{64 b^{6}}} = \sqrt[3]{\frac{11 a^{2}}{\sqrt[3]{(4 b^{2})^{3}}}}$
Note: the numerator (radical ) cannot be simplified as none of the factors 11 or a^2 is a cube. On the other hand, the denominator radical can be simplified , as it is a cube.
Now apply the rule
$\sqrt[n]{z^{k}} = (z^{k})^{\frac{1}{n}} = z^{\frac{k}{n}}$
Here, $z = 4 b^{2}, k = 3, n = 3$
So,
$\sqrt[3]{(4 b^{2})^{3}} = (4 b^{2})^{\frac{3}{3}} = 4 b^{2}$
Answer: $\sqrt[3]{\frac{11 a^{2}}{64 b^{6}}} = \frac{\sqrt[3]{11 a^{2}}}{4 b^{2}}$

Simplify the radical expression\sqrt[3]{11a^2/64b^6}

Answered question

Answer & Explanation

New Questions in Algebra I