Question

What is the simplest form of the product?
3^ sqrt 4x^2 * 3^ sqrt 8x^7


2x^3 * 3^ sqrt 4
3^ sqrt 32x^9
2x^3 * 3^ sqrt 4x^9
none of these

Answer 1

@amistre64 ; help please ? (:

Answer 2

can you place ( ) around the stuff that is inside the radicals? trying to read this is a pain

Answer 3

does 3^ sqrt mean cube root?

Answer 4

Yes .

Answer 5

sorry . . . .

Answer 6

oy vey!! its simpler if you short it as cbrt(..), or even 3rt(..)

Answer 7

3rt(4x^2) * 3rt(8x^7)

is this the problem?

Answer 8

sorry , i didnt know i could write it like that. lol

Answer 9

& yes thats the problem (:

Answer 10

hmm, it might be prudent to use an exponential form for the radicals;\[(4x^2)^{1/3} * (8x^7)^{1/3}\]

the product of an exponented thing is equal to the product of the separate terms exponented

\[4^{1/3}*(x^2)^{1/3} * 8^{1/3}*(x^7)^{1/3}\]

another property is that the exponent of and exponent is just the product of the exponents

\[4^{1/3}*x^{2/3} * 8^{1/3}*x^{7/3}\]

and rearrange

\[4^{1/3} * 8^{1/3}*x^{7/3}*x^{2/3}\]
\[\large(4*8)^{1/3}*x^{7/3+2/3}\]

Answer 11

\[\large(4*8)^{1/3}*x^{7/3+2/3}\]
\[\large(32)^{1/3}*x^{(7+2)/3}\]
\[\large\sqrt[3]{32}*x^{9/3}\]
\[\large\sqrt[3]{32}*(x^{9})^{1/3}\]
\[\large\sqrt[3]{32}*\sqrt[3]{x^{9}}\]
\[\large\sqrt[3]{32x^{9}}\]

Answer 12

now, if thats "simplest form" or not i cant determine, but its at lesast one of the answer options

Answer 13

ohhh , I see . Thank you sooo much for helping me . i have been stuck on this for sooo long . . . lol

Answer 14

\[\large\sqrt[3]{32x^{9}}=\large x^3\sqrt[3]{32}\]so its up to you what "simplest" form is :)

Answer 15

hmm, and 32 = 8*4 and 8=2^3 hmmm

Answer 16

\[\large\sqrt[3]{32x^{9}}=\large x^3\sqrt[3]{2^3*4}=2x^3\sqrt[3]{4}\]that should do it

Answer 17

gotta memorize the properties, or at least understand the underlying math that makes them work in order to recreate them ;) good luck