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mathtard
 4 years ago
Rewrite with rational exponents. Can someone please help me understand and work through this problem?
\[\sqrt[6]{xy^5z}\]
mathtard
 4 years ago
Rewrite with rational exponents. Can someone please help me understand and work through this problem? \[\sqrt[6]{xy^5z}\]

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polpak
 4 years ago
Best ResponseYou've already chosen the best response.1Ok well do they want you to rewrite it with fractional exponents? or ?

mathtard
 4 years ago
Best ResponseYou've already chosen the best response.0It says rewrite with rational exponents

simplephysics
 4 years ago
Best ResponseYou've already chosen the best response.0Okay, well sqrt6 is like a power of 1/6. Let's see if we can apply that..

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt[a]{x}=x^\frac{1}{a}\]

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1Ok. So here's basically what you need to know to do all of these problems: \[\huge \sqrt[a]{b^kc^j} = b^{\frac{k}{a}}c^{\frac{j}{a}}\]

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt[a]{b^kc^n}=(b^k c^n)^\frac{1}{a}=b^\frac{k}{a}c^\frac{n}{a}\]

mathtard
 4 years ago
Best ResponseYou've already chosen the best response.0so how do I start so I take the b and move it over? make a the denominator and make k and j the numerators?

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1The index of your radical what you will divide your powers by.

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1There's an 'is' missing from that sentence.

mathtard
 4 years ago
Best ResponseYou've already chosen the best response.0I am still confused. I don't know where to begin. I feel like all of these problems are SOOO different

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1They are not. Remember the last problem you did? \[\sqrt[4]{(5a)^4} = (5a)^{\frac{4}{4}} = (5a)^1 = 5a\]

mathtard
 4 years ago
Best ResponseYou've already chosen the best response.0It is easy to you because you understand I don't. I just don't learn that way. I need to see how it is solved. I have to actually be able to do the problem

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1So in this case we have: \[\sqrt[6]{xy^5z}\] We can rewrite it as: \[\large (xy^5z)^{\frac{1}{6}}\]

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1And the recall that when you raise a power to a power you multiply the exponents.

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1Raise a product to a power that is.

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1You just divide each of the exponents by the index of the radical.

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1What is the exponent on the x ?

phi
 4 years ago
Best ResponseYou've already chosen the best response.0Let's start at the beginning. Do you know how to write \[\sqrt{x}= x^{?}\]

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1Correct. So now divide that 1 by 6 and the new exponent on the x will be 1/6

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1Now do the same thing for the y. The exponent on the y is 5, so 5 divided by 6 is 5/6

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1Then again for the z and your result is: \[\large x^{\frac{1}{6}}y^{\frac{5}{6}}z^{\frac{1}{6}}\]

polpak
 4 years ago
Best ResponseYou've already chosen the best response.1which doesn't seem 'simpler' at all. But that's sometimes how that goes.

myininaya
 4 years ago
Best ResponseYou've already chosen the best response.0another general example of applying law of exponent: \[(x^nyz^m)^{r}=(x^ny^1z^m)^r=x^{nr}y^{1r}z^{mr}=x^{nr}y^rz^{mr}\]
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