Math(Please help)

Simplify each expression. Assume all variables are positive.

1) 3 sqrt2 - 8 sqrt128

I think you subtract the 3 from the 8 but I do not know what else to do.

2) Simplify expression. Answer should have only positive exponents.

(8x^3 y^-1/2)^2/15

Do I multiply the exponents?

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  1. ( I don't know if I'm 100% correct, could someone recheck if neeeded too? Thanks)
    1. 3sqrt2-8sqrt128 [ First you multiply 3 x 2, which will give you 6sqrt. Then you would multiply -8 and 128, which will give you -1024. The final step would be to combine like terms, the like term in the expression is 6 s q r t and - 1024 s q r t. Combining these together would give you -1018sqrt].

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  2. (1) 3sqrt2 - 8sqrt 128
    *note that 128 has factors 2 and 64 (and 64 is a perfect square), therefore:
    3sqrt2 - 8sqrt(2*64) [sqrt of 64 is 8]
    3sqrt2 - 8*8sqrt2
    -61sqrt2

    (2) distribute or multiply the exponents of each term inside the parenthesis to 2/15:
    8^(2/15) x^3(2/15) y^(-1/2)(2/15)
    8^(2/15) x^(2/5) y^(-1/15)
    *since negative exponent, we can put it in the denominator to have positive exponent
    [8^(2/15) x^(2/5)]/[y^(1/15)]

    *so there,, if you still want to simplify (factor out 1/15 from the exponents):
    (8^2 x^6 / y)^(1/15) or
    15th root of (64x^6)/y

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  3. 21b-32+7b-2ob

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