Question

Rewrite the rational exponent as a radical expression.

Answer 1

\[\left( 3\frac{ 2 }{ 3 } \right)\frac{ 1 }{ 6 }\]
A. \[\sqrt[6]{3}\]
B. \[\sqrt[9]{3}\]
C. \[\sqrt[18]{3}\]
D. \[\sqrt[6]{3^{3}}\]
Im know that the answer is either A or D

Answer 2

@campbell_st

Answer 3

well if the question is

\[(3^{\frac{2}{3}})^{\frac{1}{6}}\]

then the index law for power of a power says, multiply the powers

\[(x^a)^b = x^{a \times b}\]

and fractional powers indicate radicals

\[x^{\frac{a}{b}} = \sqrt[b]{x^a}\]

so you need to apply these 2 index laws to this problem.

hope it helps

Answer 4

remember, when you multiply 2 fractions.... simplify the answer

Answer 5

i got \[3\frac{ 5 }{ 6 }\] when I gave the exponents the same denominators and added the numerators.

Answer 6

which would be \[\sqrt[6]{3^{5}}\] .. which isnt a choice

Answer 7

remember its multiply the powers

\[\frac{2}{3} \times \frac{1}{6} = \frac{2 \times 1}{3 \times 6}\]

you need to simplify this fraction.

Answer 8

...I have to multiply them? I just gave them the same denominator of 6 and thats when I got 5/6.. So instead it would be 2/18? which i simplify to 1/9?

Answer 9

Which would make the answer B!

Answer 10

that's correct... so now the fraction indicates a radical..

the denominator is the power outside the radical

Answer 11

that's correct

Answer 12

Woaahhh! Okay that makes PERFECT sense! THANKS!