Question

Please help me solve!!!

-216^-4/3

I got -1/1296, but the software says I'm wrong. Please help!

Answer 1

May I help?

Answer 2

\[-\left( 216 \right)^{\frac{ -4 }{ 3 }}=\frac{ -1 }{ \left( 216 \right)^{\frac{ 4 }{ 3 }} }=\frac{ -1 }{ \left( 6^3 \right)^{\frac{ 4 }{ 3 }} }=\frac{ -1 }{ 6^4 }=?\]

Answer 3

-1/1296

Answer 4

??

Answer 5

or
\[(-216)^{\frac{ -4 }{ 3 }}=\frac{ 1 }{ \left( -216 \right)^{\frac{ 4 }{ 3 }} }=\frac{ 1 }{ \left\{ \left( -6 \right)^3 \right\}^{\frac{ 4 }{ 3 }} }=\frac{ 1 }{ \left( -6 \right)^4 }=? \]

Answer 6

they are different .
you know the actual statement.

Answer 7

what do you mean?

Answer 8

in the second case you get \[\frac{ 1 }{ 1296 }\]

Answer 9

Could you explain it?

Answer 10

That was wrong too. It says this is the right answer.

Answer 11

Can someone help me with another one of these?

Answer 12

it is the first one.
and I have solved above.

Answer 13

That was not the answer though. I am confused about how to arrive at the answer above.

Answer 14

@sshayer this 3 from exponent not is power of 6 bc. the denominator of an fractional exponent meaning always the index of radical and the numerator of fractional exponent is the power of this number on this fractional exponent

hope understand it now - please correct your answer - ty

Answer 15

@mathmate

Answer 16

@Blondie_B23
All the answers you and @sshayer gave are equivalent mathematically.
It seems that either your homework software is not able to do evaluation OR
you have not read or posted the complete instructions.
If the answer is given in the form you posted, it means that there are instructions like:
"express without negative exponent", or
"express without using fractional exponents", or
some other instructions.

Answer 17

Rewrite the expression below using radicals and then simplify.

Answer 18

"using radicals" would mean the radicals would remain, like \(\sqrt 2\) instead of \(2^{1/2}\)
Simplify means to put it in the simplest form (using radicals, as instructed).
"Evaluate" would give the numerical value, like what you did.

\(-216^{-4/3}\)
\(=-216^{-\frac{4}{3} }\)
\(=-\frac{1}{216^{\frac{4}{3} }}\)
\(=-\frac{1}{\sqrt[3]{216^4}}\)

Note the radical symbol was used instead of raising to the power 1/3.