How can an expression written in either radical form or rational exponent form be rewritten to fit the other form?

Question

amistre64 · Answer

by recalling the rule for it i spose

amistre64 · Answer

$$\Large \sqrt[k]{b^n}=b^{n/k}$$

gnrfan · Answer

k, I have a DBA with my teacher and it said be prepared for these types of questions

gnrfan · Answer

can you help me with another

amistre64 · Answer

maybe .. depends on what the other is

gnrfan · Answer

How can the properties of rational exponents be applied to simplify expressions with radicals or rational exponents?

amistre64 · Answer

i cant say for sure what a proper response would be for that.  How can the properties be applied?  By applying them is all i can think of to say about it.  I mean, the properties arent going to do anyone any good if they are just left sitting around collect dust.

amistre64 · Answer

the properties are just an extention of doing basic math.  they are 'shortcuts' in a way that allows us to do operations without having to redo all the middle work

gnrfan · Answer

So like "You have to apply them all to the equation to get the full use and complete the problem with them." would be fine

amistre64 · Answer

im not sure what would be fine :)

amistre64 · Answer

i can math, writing complete sentences for math is not my strong point

gnrfan · Answer

complete opposite for me. Another or no?

amistre64 · Answer

i can try another, but unless its a mathing problem i might not be able to be much use

gnrfan · Answer

some help is better than none. 
    What reasoning and explanations can be used when solving radical equations?
    How do extraneous solutions arise from radical equations?

amistre64 · Answer

your material might have a better answer for these, but i would say:

radical equations are just exponent equation in disguise, so using properties of exponents may be useful.

extra solutions tend to arise because when we attempt to get rid of a radical, we are messing around with a restricted domain and altering it.

amistre64 · Answer

for example:

sqrt(2x-4) = x+8

we can square each side to get rid of the radical

2x-4 = x^2+16x+64

the solutions to the new problem are from a different domain than the original setup.  so we have to test our solutions to see what fits in the original

gnrfan · Answer

k, thanks for ur help. i know these aren't easy

amistre64 · Answer

youre welcome.  the site is acting up for me so communicating is not going so smoothly on my end at least.  good luck with it all :)