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?

( 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].

(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

21b-32+7b-2ob

To simplify each expression, we can use the properties of radicals and exponents.

1) 3√2 - 8√128

First, we simplify the radicals. Notice that 128 can be written as 64 * 2. So, we have:
3√2 - 8√(64 * 2)

Since the square root of 64 is 8, we can simplify further:
3√2 - 8 * 8 * √2

Multiplying, we have:
3√2 - 64√2

Now, we can combine the like terms (the terms with the same radical):
(3 - 64)√2

Simplifying the coefficients, we get the final answer:
-61√2

Therefore, 3√2 - 8√128 simplifies to -61√2.

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

To simplify this expression, we use the property of exponents that states when you raise a power to another power, you multiply the exponents.

In this case, we have a fraction as the exponent, so we'll first simplify the exponent:
2/15 = 1/7.5 = 2/3 * 1/5 = 2/3 * 1/√(5^2) = 2/√(3^2 * 5^2) = 2/√(225) = 2/15

Now, we apply this exponent to every term within the parentheses:
(8^(2/15) * x^(3 * 2/15) * y^(-1/2 * 2/15))

Simplifying each term separately:
8^(2/15) = √(8^2) = √64 = 8

x^(3 * 2/15) = x^(6/15) = x^(2/5)

y^(-1/2 * 2/15) = y^(-1/30)

Putting it all together:
(8 * x^(2/5) * y^(-1/30))

Finally, we rearrange the terms to bring the negative exponent to the denominator (remember that a negative exponent is equivalent to 1 divided by the positive exponent):
(8 * x^(2/5) / y^(1/30))

Therefore, the simplified expression is 8x^(2/5) / y^(1/30).