Question is Simplify 625^3/4. answer is 125.
What isn't the answer +/-125?
well, I suppose I would check
-125^4/3
-125^1/3 = -5
then(-5)^4 = 625
so it looks like you are right to me
625^3/4
= (√ (√625) )^3
= (√25)^3
= 5^3
= 125
by definition of the square root operation:
return the positive square root of the number
e.g. √4 = 2 , even your calculator is programmed that way
as opposed to
x^ = 4
We usually write as our next step
x = ± 2
skipping the all important steps between:
x^2 = 4
±x = √4
±x = 2 ----> x = 2 OR -x = 2, which is
x = ± 2
This is critical in statements such as
x^2 > 4
It would be incorrect to say x > ± 2
instead we have to say:
x^2 > 4
±x > 2
thus x > 2 OR -x > 2
giving us the correct solution :
x > 2 OR x < -2
The answer to the expression 625^(3/4) is not +/-125.
To simplify the expression, we need to take the fourth root of 625 and then raise it to the power of 3.
The fourth root of 625 can be found by raising 625 to the power of 1/4.
625^(1/4) = 5.
Now, we raise 5 to the power of 3 to get the final result:
5^3 = 5 * 5 * 5 = 125.
So, the simplified answer is 125.
The answer to the question "Simplify 625^(3/4)" is indeed 125. However, it's important to note that there is only one correct answer in this case because we are dealing with real numbers.
When we simplify an expression with an even root (such as ^1/2, ^1/4, etc.), we take the principal root, which is the positive value. Therefore, when we simplify 625^(3/4), we need to take the principal fourth root of 625. The principal fourth root of 625 is 5, so 625^(3/4) simplifies to 5^3, which is equal to 125.
If we were dealing with an odd root (such as ^1/3, ^1/5, etc.), then both positive and negative values would be valid answers. However, in this case, since the root is even, there is only one correct answer, which is 125.