Answer:
The correct answer is B. [tex]\sqrt[9]{3}[/tex]
Step-by-step explanation:
The root of a number can be expressed as the number raised to the power whose exponent is a fractional number. The exponent number will be the inverse of the root index.
In this case, three to the two thirds power all raised to the one sixth power is expressed as:
[tex](3^{\frac{2}{3} }) ^{\frac{1}{6}}[/tex]
Power of a Power Property: This property states that the power of a power can be found by multiplying the exponents.
So, we multiply the exponents:
[tex]\frac{2}{3} \times \frac{1}{6}= \frac{1}{9}[/tex]
The expression would be:
[tex]3^{\frac{1}{9} }[/tex]
which as a radical expression is:
[tex]\sqrt[9]{3}[/tex]
The four options are expressed as:
a) [tex]\sqrt[6]{3}[/tex]
b) [tex]\sqrt[9]{3}[/tex]
c) [tex]\sqrt[18]{3}[/tex]
d) [tex]\sqrt[6]{3^3}[/tex]
The correct answer is B.
