Question

10.........................

Answer 1

Hello!

The answer is:

a. $a^{\frac{3}{2}}bc^{2}$

Why?

To simplify the expression, we need to transform the radical into a exponential form, then apply the exponential property.

Transforming radical to exponential form:

$\sqrt[n]{x}=x^{\frac{1}{n}}\\\sqrt{x}=x^{\frac{1}{2} }$

Power of a power property:

$(a^{m})^{n}=a^{mn}\\\\(a^{m})^{\frac{1}{n}}=a^{\frac{m}{n}}$

So,

$\sqrt[4]{a^{6}b^{4}c^{8}}=(a^{6}b^{4}c^{8})^{\frac{1}{4}}\\\\(a^{6}b^{4}c^{8})^{\frac{1}{4}}=a^{\frac{6}{4}}b^{\frac{4}{4}}c^{\frac{8}{4}}\\\\a^{\frac{6}{4}}b^{\frac{4}{4}}c^{\frac{8}{4}}=a^{\frac{3}{2}}bc^{2}$

Have a nice day!