Math people can you check if i got these right!

[waloshin]

1) Express each of the following as a power of 2 and then simplify.

A) (cubed root √4)^6 = (4) ^6/4 = (2^2) 6/4 = 2^12/4 = 2^3

B) (1/64)^5/6 = (1/2^6)^5/6 = (2 ^-6)^5 = 26^-30 = 1/2^30

2) Simplify the following radicals completely.

A) 4th root √32 = 4th root 2√2

B) 4th root √ 81x^8 z^6
_______________
w^12

= 3x^2 z^4 √x^2
________________
w^12

 

[Doctor Q]

It's a bit hard to read the notation in a text post, but in general the steps you want to do are as follows:

• Change roots to exponential form, i.e., change √x to x^(1/2), change cube root of x to x^(1/3), change fourth root of x to x^(1/4), etc.
• If the problem involves raising 4 to a power, change the 4 to 2^2. If it involves raising 8 to a power, change the 8 to 2^3. And so on for 16, 32, 64, ....
• Repeatedly use the rule that (x^n)^m = x^(nm), to combine exponents.

Example:

(Cube root of 32)^4 = (32^(1/3))^4 = ((2^5)^(1/3))^4 = 2^(5 x 1/3 x 4) = 2^(20/3)​

Does that help you solve the problems in your assignment?