We can often multiply and divide radicals with different indexes.For example: $$\sqrt { 3 } \sqrt [ 3 ] { 5 } = \sqrt [ 6 ] { 27 } \sqrt [ 6 ] { 25 } = \sqrt [ 6 ] { ( 27 ) ( 25 ) } = \sqrt [ 6 ] { 675 }$$
Use this idea to write the following expression as a single radical.
$\frac { \sqrt [ 6 ] { 4 } } { \sqrt { 5 } }$
A) $\quad \frac { \sqrt [ 6 ] { 500 } } { 9 }$
B) $\frac { \sqrt [ 6 ] { 500 } } { 5 }$
C) $\frac { \sqrt [ 6 ] { 500 } } { 4 }$
D) $\frac { \sqrt [ 7 ] { 500 } } { 5 }$

Question

Quizplus · Accepted Answer

We can write $$\frac { \sqrt [ 6 ] { 4 } } { \sqrt { 5 } } = \sqrt [ 6 ] { \frac {4}{5}} = \sqrt [ 6 ] { \frac {4 \cdot 125}{5 \cdot 125}} = \sqrt [ 6 ] { \frac {500}{5^6}} = \boxed{\frac { \sqrt [ 6 ] { 500 } } { 5 }}$$

We Can Often Multiply and Divide Radicals with Different Indexes 353=276256=(27)(25)6=6756\sqrt { 3 } \sqrt [ 3 ] { 5 } = \sqrt [ 6 ] { 27 } \sqrt [ 6 ] { 25 } = \sqrt [ 6 ] { ( 27 ) ( 25 ) } = \sqrt [ 6 ] { 675 }3​35​=627​625​=6(27)(25)​=6675​

We Can Often Multiply and Divide Radicals with Different Indexes $\sqrt { 3 } \sqrt [ 3 ] { 5 } = \sqrt [ 6 ] { 27 } \sqrt [ 6 ] { 25 } = \sqrt [ 6 ] { ( 27 ) ( 25 ) } = \sqrt [ 6 ] { 675 }$