Question

simplifying radicals with exponent's . PLeASE HELP!!

Answer 1

?

Answer 2

\[\sqrt[6]{125}x^3y^9z^6\]

Answer 3

\(\Large\sqrt[6]{125}x^3y^9z^6\)
Are the variables supposed to be outside the radical?

Answer 4

yea I'm guess you single pair it by 6 and the radical exponents

Answer 5

This is the problem?
\(\Large\sqrt[6]{125x^3y^9z^6}\)

Answer 6

yes.

Answer 7

Ok. Look at the following:
\(\Large\sqrt[n]{a^n} = a\)
For example, \(\Large \sqrt[4]{x^4} = x\) (for non-zero x).

Answer 8

In your problem, \(125 = 5^3\)
There aren't enough factors of 5 inside the radical to take a 6th root, so 125 remains.
The same is true of \(x^3\)

Answer 9

\(\Large \sqrt[6]{z^6} = z\)

Answer 10

Now we need to deal with y.
\(\Large y^9 = y^{6 + 3} = y^6 \cdot y^3\)

Answer 11

wouldn't make it \[\sqrt{z^6}\] ?

Answer 12

so the exponents subtract?