solve [(root125)^4]^1/6. so far, I got (6 root root 125)^25 is this correct? Where do I go from here? how can I get rid of two roots?
please help me understand this; I have ten more math problems that are similar to still do.
I assume you want to evaluate
[(root125)^4]^1/6 , not "solve" it
recall that (a^x)^y = a^xy
so we get
(root125)^4/6
= ((125)^1/2)^2/3
= 125^1/3
= 5
oh, okay, thanks!
To solve the expression [(√125)^4]^(1/6), let's break down the steps:
Step 1: Simplify the inner exponent (√125)^4.
- (√125)^4 is equivalent to (125)^(1/2 * 4) since (√x)^2 is x.
- Calculating (125)^(1/2 * 4) gives us 125^2.
Step 2: Simplify the outer exponent 125^2^(1/6).
- 125^2^(1/6) means we need to take the 6th root of 125^2.
- We can rewrite it as (125^2)^(1/6).
- (125^2)^(1/6) simplifies to 125^(2 * 1/6).
Step 3: Calculate 125^(2 * 1/6).
- To calculate 125^(2 * 1/6), we multiply the exponents together.
- 2 * 1/6 gives us 2/6, which simplifies to 1/3.
- Therefore, 125^(2 * 1/6) is equivalent to 125^(1/3).
So the final simplified expression is 125^(1/3).
To answer your question about how to get rid of two roots, it seems that you made a mistake while simplifying the expression. The correct step is to calculate 125^(1/3) instead of [(6√√125)^25].
To evaluate 125^(1/3), you can use a calculator, which will give you 5 as the answer.