Question

http://prntscr.com/ajownu

Answer 1

what number to the fifth power is -243?

Answer 2

if you don't know that, do you know at least one factor of -243 besides -1 and 1?

Answer 3

9

Answer 4

ok cool and what is 243 divided by 9

Answer 5

27

Answer 6

\[243=9 \cdot 27\]
but both 9 and 27 can be written as powers of 3

Answer 7

for example 9 is 3^2

27 is 3^?

Answer 8

do you know what exponent completes that last sentence ?

Answer 9

9

Answer 10

27 is 3^9 ?

Answer 11

3^2=3*3=9
3^3=3*3*3=9(3)=27

Answer 12

27 is 3^3

Answer 13

\[243=9 \cdot 27=3^2 \cdot 3^{3}=3^{5} \\ -243=-1(243)=(-1)^5(3)^5=(-1 \cdot 3)^5=(-3)^5\]


\[\sqrt[5]{a^5}=a\]
and we have
\[\sqrt[5]{(-3)^5}=?\]

Answer 14

243?

Answer 15

did you see my line
\[\sqrt[5]{a^5}=a\]
?

Answer 16

example:
\[\sqrt[5]{4^5}=4\]

Answer 17

another example
\[\sqrt[5]{(-81)^5}=-81\]

Answer 18

\[\sqrt[5]{(-3)^5}=?\]

Answer 19

-243

Answer 20

no the 5th root of -243 isn't -243....

Answer 21

\[\sqrt[5]{32}=2 \text{ since } 2^5=32\]
in words:
the 5th root of 32 is 2 since 2 to the power of 5 is 32

Answer 22

the whole reason we wrote -243 as some number to the 5th power
so we can basically cancel out the power and the root part

Answer 23

this is why you see me write \[\sqrt[5]{a^5}=a\]

Answer 24

so do you think you can try to use that now:
\[\sqrt[5]{(-3)^5}=?\]

Answer 25

I gave examples above too...
but if you need more examples:

\[\sqrt[5]{(-7)^5}=-7 \\ \sqrt[5]{6^5}=6\]

Answer 26

oh its -3?

Answer 27

yes the 5th root of -243 is -3 since (-3) to the fifth power is -243