Question

Which expression is equivalent to

Answer 1

\[\sqrt[3]{27n^5m^3p^2}\]

Answer 2

A) \[2n^\frac{ 3 }{ 5 }mn^ \frac{ 2 }{ 3}\]

Answer 3

recall the cubed root is the same as to the 1/3 power

Answer 4

quick note

Answer 5

and @DanJS notes faster than me lol

Answer 6

\[[27n^5m^3p^2]^{1/3}\]

Answer 7

you dont have to write the answers out, we can figure it out

Answer 8

Oh okay

Answer 9

do you remember

\[[x^a]^b = x ^{a*b}\]

Answer 10

a power raised to another power, you can multiply the powers together

Answer 11

Yes i think ,

Answer 12

\[27^{1/3} * n ^{5 * 1/3} *m ^{3 * 1/3} * p ^{2*1/3}\]

you see how each power was multiplied by 1/3

Answer 13

for example

\[[n^5]^{1/3} = n ^{5 * 1/3} = n ^{5/3}\]

Answer 14

Yes i see.

Answer 15

ok , do that for the other 2 variables, m and p

Answer 16

and for the 27, it probably would be easier to understand leaving it as a cubed root rather than to the 1/3 power

cubed root of 27 means, "what number multiplied by itself 3 times is 27"

Answer 17

27 = x * x * x

Answer 18

3 ?

Answer 19

right , so
\[\sqrt[3]{27} = 3\]and we found the n is n^(5/3)

Answer 20

now you just have to multiply the m and p variables powers by 1/3 also

Answer 21

\[\sqrt[3]{27} * n ^{5/3} *m ^{3/3} * p ^{2/3}\]

Answer 22

just have to simplify those

Answer 23

m^(3/3) = m^1 = m

Answer 24

p^(2/3) is simplified as much as you can

Answer 25

Thank you so much i really appreciate it.

Answer 26

cool, you understand the two rules used here?

nth root of a quantity is the same quantity to the 1/nth power

variable raised to a power raised to a power = variable raised to the powers multiplied

Answer 27

Yep

Answer 28

cool, glad to help