Question

Write in simplest radical form

Answer 1

\[\sqrt[4]{27}\times \sqrt[8]{9}\]

Answer 2

@mathmale so does the 4 become (to the 1/4 power) and the 8 (to the 1/8) power?

Answer 3

yes

Answer 4

When I did this on Mathway, I got \[27^{0/4}\]

Answer 5

\[27^{1/4}*9^{1/8}\]

Answer 6

So that's as far as you can possibly go? They didn't say to solve, just write in simplest radical form

Answer 7

just keep going

Answer 8

\[(27*9)^{1/4+1/8}\]

Answer 9

\[243^{3/8}\]

Answer 10

The answer is 3!

Answer 11

\[\sqrt[8]{243^{3}}\]

Answer 12

Strong suggestion: Rewrite your\[\sqrt[4]{27}\times \sqrt[8]{9}\]as\[27^\frac{ 1 }{ 4 }*9^{\frac{ 1 }{ 8 }}\]

Answer 13

Recognize that this result is the same as \[(3^3)\ ^{ \frac{ 1 }{ 4 }}*(3^2)^{\frac{ 1 }{ 8} }\]

Answer 14

See if you can simplify this.

Answer 15

Hints:\[(a^x)^y=a ^{xy}\]and\[a^x*a^y=a ^{x+y}\]

Answer 16

So it would be \[(3^{5})^{3/8}\]

Answer 17

\[243^{3/8}\]

Answer 18

\[(3^3)\ ^{ \frac{ 1 }{ 4 }}*(3^2)^{\frac{ 1 }{ 8} }\] simplifies to \[3^{3/4 }*3^{1/4}\] Please check that out and then simplify this last expression.

Compare your result to 243^(3/8).

Answer 19

\[3^{4/4}\] which equals 3

Answer 20

does that agree with any of your answer choices?

Answer 21

This one wasn't multiple choice, they just wanted me to write the problem in simplest radical form in the blank! But I've never done one like this before, so seeing the steps to solve it really helps a lot. Thank you so much

Answer 22

You're very welcome, and I hope to have the pleasure of working with y ou again!