Question

Hi there!

Can I get some help with this calculus homework. #6a and 8b. Don't forget to show your work! Thank you! ​

Answer 1

6a. -8

8b. 1/125

Explanation:

If you know powers of 2 and the squares and cubes of small integers, you can work these in your head. There is no "work" to show. Of course, a calculator can evaluate these easily. (see attached)

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6a. (-128)^(3/7) = ((-2)^7)^(3/7) = (-2)^3 = -8

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8b. (27^(2/3) +8^(4/3))^(-3/2) = ((3^3)^(2/3) +(2^3)^(4/3))^(-3/2)

= (3^2 +2^4)^(-3/2) = (9+16)^(-3/2) = 25^(-3/2)

= (5^2)^(-3/2) = 5^(-3) = 1/5^3

= 1/125