Which of the following are equivalent? Justify your reasoning Wait till i draw all the options

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Which of the following are equivalent? Justify your reasoning Wait till i draw all the options

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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|dw:1438040615062:dw|
What does choice B simplify to?

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Other answers:

x1?
x^1 you mean? if so, then yes x^1 = x |dw:1438041275973:dw|
how about choice C?
ya that
how do you simplify tht? add?
|dw:1438041368560:dw|
Due to the rule \[\LARGE x^a*x^b = x^{a+b}\]
|dw:1438041074473:dw|
good
wait 3x
so C is not equal to A, and not equal to B
no there's no 3x
oh ok
|dw:1438041475304:dw|
ok i see
now simplify D
so you just add the top right so 3/3?
is there 3x for this
yeah 1/3+1/3+1/3 = (1+1+1)/3 = 3/3
no 3x
x*x = x^2 NOT x*x = 2x
so x3/3 only?
\[\Large x^{1/3}*x^{1/3}*x^{1/3} = x^{1/3+1/3+1/3}\] \[\Large x^{1/3}*x^{1/3}*x^{1/3} = x^{(1+1+1)/3}\] \[\Large x^{1/3}*x^{1/3}*x^{1/3} = x^{3/3}\] \[\Large x^{1/3}*x^{1/3}*x^{1/3} = x^{1}\] \[\Large x^{1/3}*x^{1/3}*x^{1/3} = x\]
|dw:1438041705953:dw|
so b and d are equivalent?
correct
so how do i justify the reasoing
You're simplifying each expression using the rule \[\LARGE x^a*x^b = x^{a+b}\]
for part B, you also use the fact that \[\Large \frac{1}{x^{-k}} = x^k\]
ok thanks!
no problem
i will just out it in words

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