Question

Simplify 2^1/3 times 4^1/3 using the radical form

Answer 1

A. 512 B. 2^2/3 C. 2. D. 8

Answer 2

rewrite the 2nd one in terms of a common base with the 1st term

use the following information: \(\huge (a^b)^c=a^{(b*c)}\\\huge a^b*a^c=a^{(b+c)}\)

Answer 3

Ok

Answer 4

It would be 8

Answer 5

I didn't get that, show your work

Answer 6

Well I multiplied 4 and 2 and got 8
1/3=1/3 so I left it that way

Answer 7

you can't do that. that's why I said you had to convert it.
\(\huge (a^b)^c=a^{(b*c)}\\\huge a^b*a^c=a^{(b+c)}\)
note that the bases are the same for the 2nd equation. that means we have to rewrite 4 as a po wer of 2

Answer 8

Ok so the exponents would equal 2/3

Answer 9

not really, you're not listening to what I'm saying.

\(\large 4^\frac{1}{3}=2^?\)

Answer 10

\(\Large {\bf
2^{\frac{1}{3}}\cdot 4^{\frac{1}{3}}\qquad {\color{brown}{ 4=2^2}}\qquad 2^{\frac{1}{3}}\cdot (2^2)^{\frac{1}{3}}\implies (2)^{2\cdot \frac{1}{3}}
}\)

can you see wht bibby is saying now?

Answer 11

1/3?

Answer 12

lol, sorry, I'm never sure what I should illustrate and what I should be explaining. thanks jode

anyhow, if \( 4=2^2\) and \(\large(a^b)^c=a^{(b*c)}\) then \(4^frac{1}{3}=(2^2)^\frac{1}{3}\)

Answer 13

Thank you both

Answer 14

\(\huge 2^\frac{1}{3} \times 2^\frac{2}{3}=?\)

Answer 15

2