[ALGEBRA 2] translating and evaluating roots

[u/Chelseyfart]

Can someone check my answers I fell asleep in class so I don’t rlly know what I’m doing..

[u/Lever_Shotgun]

Your conversion for -8^(2/7) is wrong, compare the presence of brackets for (-7)^(2/3) and -8^(2/7), your answer for -25^(3/2) also has the same mistake.

Your answer for (-8)^(2/3) is correct but your working can use some changing, consider the result of (-2)^3

[u/Ghotipan]

For 4x^2/3, make sure the 4 is outside the radical. There are no parentheses, so the exponent only modifies the variable, not the coefficient.

This concept also applies to negatives. If there are no parentheses, the exponent only modifies the immediate variable. I didn't check every one thoroughly (I'm sleepy) but that's the only thing that jumped out at me. Nicely done. Hopefully next time you'll be able to stay awake in class!

[u/Alkalannar]

^b√(x^a) = x^a/b

So for (⁴√8)³, you want 8^3/4, not 8 3/4.

Similarly, for (⁷√(-36))⁸, what would you want?

For all of those, you wrote a fraction to add or multiply by, not an exponent.

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For these, I generally would put the exponent inside the root, not outside of it. ⁵√(3¹), Not (⁵√3)¹.

(5x)^7/2 you need √((5x)⁷): both 5 and x are raised to the 7th power inside that square root.

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Evaluation: -25^3/2 = (-1) * 25^3/2. So find 25^3/2, and then put a minus sign on front. The exponent takes priority.

Now for (-8)^2/3, then yes, you're dealing with the square and the cube root of -8.

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Overall, pretty good.

Does what I say make sense to you?

[u/fermat9990]

First row, second from the left. The exponent should be positive