Question

Simplifying radicals help! Medal to best answer!!







Question will be posted below.

Answer 1

\[\sqrt[3]{4/9}\]

Answer 2

It needs to be simplified and I'm not sure how to do that with a fraction.

Answer 3

@Directrix could you help maybe?

Answer 4

rewrite them in index form

\[\sqrt[3]{\frac{4}{9}} = \sqrt[3]{(\frac{2}{3})^2} = \sqrt[3]{2^2 3^{-2}}\]

now apply the index rule for the cube roots...

\[\sqrt[a]{x} = x^{\frac{1}{a}}\]

Answer 5

Thanks campbell! So now I do:
\[\sqrt[3]{2^2*1/3 * 3^2*1/3}\]

Answer 6

@campbell_st

Answer 7

no its

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

just simplify this

Answer 8

but it doesn't come out as a whole number?

Answer 9

I am just supposed to simplify.

Answer 10

you need the index law for power of a power.... which requires you to multiply the powers

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

you need to use this law to finish this question

Answer 11

so like this?

\[2^{2/3}*3^{-2/3}\]

Answer 12

@campbell_st

Answer 13

that's correct.... it can be written with out the multiplication.

Answer 14

I need the final answer to be written as a fraction and with a square root. Can you help with that? thanks.

Answer 15

@campbell_st

Answer 16

if its as a fraction with a cube root its simply

\[\sqrt[3]{\frac{2^2}{3^2}}\]

Answer 17

That is not one of my options....here they are:

\[\frac{ \sqrt[3]{12} }{ 3 }\]

\[\frac{ \sqrt[3]{324} }{ 9 }\]

\[\frac{ \sqrt[3]{5} }{ 3 }\]

\[\frac{ \sqrt[3]{36} }{ 9 }\]

Answer 18

@campbell_st

Answer 19

@Directrix I really need some assistance. Thanks!

Answer 20

@mathstudent55 @dan815 @Mimi_x3 @Abhisar @TheSmartOne @CGGURUMANJUNATH Can someone help me please?

Answer 21

Where is the question? @BeccaB003

Answer 22

Here it is:
Simplify:
\[\sqrt[3]{\frac{ 4 }{ 9 }}\]

Answer 23

the answer options are the fifth one up that I already posted.