Question

URGENT: can someone help me solve this ASAP

The cube root of 4 times the sixth root of 8

3sqrt4•6sqrt8

I'm really confused here. Thanks

Answer 1

Using a calculator, the cube root of 4 is approximately 1.58740105197.

Answer 2

Also, the sixth root of 8 is approximately 1.41421356237.

Answer 3

Multiply: 1.58740105197*1.41421356237=2.2449240966
So, the cube root of 4 times the sixth root of 8 is approximately equal to 2.2449240966

Answer 4

\[4^{\frac{ 1 }{ 3 }}\times8^{\frac{ 1 }{ 6 }}\]

Answer 5

I turned them into fraction format and got 32^5/6 but do I simplify it anymore?

Answer 6

Oh, I thought you wanted this in decimal format.

Answer 7

How did you get 5/6?

Answer 8

I'm not sure what to do after this step.

Answer 9

So it's easier if you set both 4 and 8 to 2 to the power of something

Answer 10

I created a common denominator 4^2/3 times 6 and 8^1/6 times 3 to get the final as 32^ 5/6

Answer 11

After simplified

Answer 12

\[4=2^{2} and 8=2^{3}\]

Answer 13

Wait I carried the wrong number. It's supposed to be 1/3 not 2/3

Answer 14

Using that you can have a common value that is being raised to some exponent

Answer 15

Okay the exponents seem understandable but what about the fraction forms? Do you add that to the exponent?

Answer 16

So \[4^{\frac{ 1 }{ 3 }}=2^{\frac{ 2 }{ 3 }}\]
and \[8^{\frac{ 1 }{ 6 }}=2^{\frac{ 3 }{ 6}}\]

Answer 17

So after you change the fraction so that you have a common denominator, you should be getting \[2^{\frac{ 7 }{ 6 }}\]

Answer 18

Oh okay I understand

Answer 19

And the answer should be 2 times the sixth root of 2

2• 6sqrt2

Answer 20

Wait question

Answer 21

Technically that's correct but that wouldn't be the most simplified form

Answer 22

Why don't you multiply the 2 to get 4?

Answer 23

What's the question?

Answer 24

4^7/6

Answer 25

It's an exponent rule
Well you can solve it out for proof as to why you can't just multiply the 2's to get 4
Let's pretend that your exponent isn't a fraction but a whole number (since it's easier to understand)
EXAMPLE
\[2^{3}\times2^{2}=8\times4=32\]

If you had multiplied the 2's together and said that
\[2^{3}\times2^{2}=4^{5}\]
that would not be equal to 32 (which is the correct answer)

Answer 26

And 2^5=32

Answer 27

Oh alright. Thank you so much for being patient with me and helping me. I understand everything now. Thank you!!!

Answer 28

np :)