how would you solve [(*square root*125)^4]^1/6
The "square root" of a number simply means the number is raised to the power of 1/2 or 0.5.
So your question becomes (((125)^1/2)^4)^1/6
When you have exponents beside each other you simply multiply them.
So the question becomes 125^(0.5*4*1/6)
= 125^(1/3)
Now what number multiplied by itself 3 times gives you 125?
5^3 = 125, but now what do i do?
5^3 = 125
So how do we get 125^(1/3) from this?
Simply take the cubed root of both sides.
(5^3)^(1/3) = 125(^1/3)
What then, must the cubed root of 125 be?
five. got it now thanks so much
No problem :)
To solve the expression [(*square root*125)^4]^1/6, we need to simplify it step-by-step according to the rules of exponentiation and the order of operations.
Let's break it down:
Step 1: Simplify the square root of 125.
The square root of 125 can be simplified as √125 = 5√5.
Step 2: Raise the simplified square root to the power of 4.
(5√5)^4 can be expanded as (5^4) * (√5)^4.
Since 5^4 equals 625, we have: 625 * (√5)^4.
Step 3: Simplify the (√5)^4.
Since (√5)^2 equals 5, we can simplify (√5)^4 as (5)^2.
Thus, we have: 625 * (5)^2.
Step 4: Evaluate the power of 5 squared.
Calculating 5^2 gives us 25.
Therefore, the expression simplifies to: 625 * 25.
Step 5: Multiply the values.
Multiplying 625 by 25 results in 15625.
So, the solution to the expression [(*square root*125)^4]^1/6 is 15625.