Answer:
The answer is (a) ⇒ [tex]a^{\frac{3}{2}}bc^{2}[/tex]
Step-by-step explanation:
* Lets revise the rational exponent
- [tex]\sqrt[n]{x^{m}}=x^{\frac{m}{n}}[/tex]
* So we can change any radical to a rational exponent
* Lets solve our problem
∵ [tex]\sqrt[4]{a^{6}b^{4}c^{8}}[/tex]
* Lets simplify each one
- The first is root 4 of a to the power of 6, we will change the root
and the power to rational exponent 6/4
∴ [tex]\sqrt[4]{a^{6}}=a^{\frac{6}{4}}[/tex] ⇒ simplify the fraction
∴ [tex]\sqrt[4]{a^{6}}=a^{\frac{3}{2}}[/tex]
- The second is root 4 of b to the power of 4, we will change
the root and the power to rational exponent 4/4 = 1
∴ [tex]\sqrt[4]{b^{4}}=b^{\frac{4}{4}}=b^{1}=b[/tex]
- The third is root 4 of c to the power of 8, we will change
the root and the power to rational exponent 8/4 = 2
∴ [tex]\sqrt[4]{c^{8}}=c^{\frac{8}{4}}=c^{2}[/tex]
* The simplest form of [tex]\sqrt[4]{a^{6}b^{4}c^{8}}=a^{\frac{3}{2}}bc^{2}[/tex]
