Question

(^3sqrtc^7d^4)^2

Answer 1

so the problem is this?

\[\LARGE \left(\sqrt[3]{c^7d^4}\right)^2\]

Answer 2

Yes

Answer 3

and they want you to simplify? or rewrite into rational exponent form?

Answer 4

simplify

Answer 5

ok are you familiar with converting radical form to rational exponent form?

Answer 6

not at all

Answer 7

I'm going to use this rule

\[\LARGE \sqrt[n]{x^m} = x^{m/n}\]

hopefully it looks familiar

Answer 8

ok... walk me through how to solve this

Answer 9

so we use that rule to go from

\[\LARGE \sqrt[3]{c^7d^4}\]
to
\[\LARGE \left(c^7d^4\right)^{1/3}\]

Answer 10

ok

Answer 11

which is why

\[\LARGE \left(\sqrt[3]{c^7d^4}\right)^2\]
is the same as
\[\LARGE \left(\left(c^7d^4\right)^{1/3}\right)^2\]

Answer 12

ok

Answer 13

then we multiply the exponents
\[\LARGE \left(\left(c^7d^4\right)^{1/3}\right)^2\]
\[\LARGE \left(c^7d^4\right)^{1/3*2}\]
\[\LARGE \left(c^7d^4\right)^{2/3}\]

Answer 14

ok

Answer 15

so do you see how I got \[\LARGE \left(c^7d^4\right)^{2/3}\]

Answer 16

yes

Answer 17

now we multiply the inner exponents by the outer exponent 2/3

\[\LARGE \left(c^7d^4\right)^{2/3}\]
\[\LARGE c^{7*2/3}d^{4*2/3}\]
\[\LARGE c^{14/3}d^{8/3}\]

Answer 18

when you divide 14/3, what is the quotient and remainder?

Answer 19

I think it would be 14 is youre remainder and 3 is youre quotient

Answer 20

14/3 = 4 remainder 3

4 is the quotient, 3 is the remainder

Answer 21

that leads us to

\[\LARGE c^{14/3} = c^4\sqrt[3]{c^2}\]

Answer 22

similarly,

\[\LARGE d^{8/3} = d^2\sqrt[3]{d^2}\]

Answer 23

so overall

\[\LARGE c^{14/3}d^{8/3} = c^4\sqrt[3]{c^2}*d^2\sqrt[3]{d^2}\]

\[\LARGE c^{14/3}d^{8/3} = c^4d^2\sqrt[3]{c^2d^2}\]

Answer 24

sorry I meant to say "14/3 = 4 remainder 2" (not remainder 3)

Answer 25

Thank you :) could you help with a couple more

Answer 26

I'll help with one more. Please post where it says "ask a question" so you can start a new post