Question

i need help with simplifying an expression

Answer 1

post it

Answer 2

\[\sqrt[4]{256x ^{16}}\]

assume that all variable are positive

my answer sheet says the answer is \[4z ^{4}\]

Answer 3

\[\left(256 x^{16}\right)^{\frac{1}{4}}\]

Answer 4

\[256^{\frac{1}{4}} x^4\]

Answer 5

wait. why did you change it to 1/4th

Answer 6

\[a^{1/4}=\sqrt[4]{a}\]

Answer 7

\[(a b)^{\frac{1}{4}}=a^{\frac{1}{4}}b^{\frac{1}{4}}\]

Answer 8

im sorry but im not following you

Answer 9

what seems troubling?

Answer 10

i dont understand your first step. how does that work?

Answer 11

You can rewrite
\[\sqrt[4]{a}\]

as
\[a^{1/4}\]

Answer 12

ok so then you divide the ^16 by 1/4 and get 256^1/4 x^4 ?

Answer 13

According to rule above , I can rewrite as follows:\[\left(256 x^{16}\right)^{\frac{1}{4}}\]

Using another rules which states:
\[(a b)^{\frac{1}{4}}=a^{\frac{1}{4}}b^{\frac{1}{4}}\]

we can change our expression into
\[\left(256^{\frac{1}{4}} \left(x^{16}\right)^{\frac{1}{4}}\right)\]

Answer 14

\[\large \sqrt[4]{256x^{16}}\]



\[\large \left(256x^{16}\right)^{\frac{1}{4}}\]



\[\large \left(256\right)^{\frac{1}{4}}\left(x^{16}\right)^{\frac{1}{4}}\]



\[\large \sqrt[4]{256}\left(x^{16}\right)^{\frac{1}{4}}\]



\[\large \sqrt[4]{4^4}\left(x^{16}\right)^{\frac{1}{4}}\]



\[\large 4\left(x^{16}\right)^{\frac{1}{4}}\]



\[\large 4x^{16*\frac{1}{4}}\]



\[\large 4x^{\frac{16}{4}}\]



\[\large 4x^{4}\]

So \[\large \sqrt[4]{256x^{16}}=4x^{4}\]

Answer 15

why does the \[\sqrt[4]{?}\] come back on the fouth step?

Answer 16

I converted back to radical notation because I wanted to take the 4th root of 256 (or 4^4) to get 4

Answer 17

thanks again :)