-pangkat-3%2F4.jpeg "(1/10.000) Pangkat 3/4")
Raising a Fraction to a Fractional Power
In mathematics, raising a fraction to a fractional power may seem like a daunting task, but it's actually a straightforward process. In this article, we'll explore how to raise (1/10,000) to the power of 3/4.
Understanding Fractional Exponents
Before we dive into the calculation, let's quickly review what fractional exponents are and how they work.
A fractional exponent is a fraction that is used as an exponent. It's a way of expressing a power that is not a whole number. For example, x^(1/2) is equivalent to the square root of x.
Raising (1/10,000) to the Power of 3/4
Now, let's raise (1/10,000) to the power of 3/4. To do this, we can use the formula:
x^(a/b) = (x^a)^(1/b)
In our case, x = 1/10,000, a = 3, and b = 4. Plugging these values into the formula, we get:
(1/10,000)^(3/4) = ((1/10,000)^3)^(1/4)
Simplifying the Expression
To simplify this expression, we need to follow the order of operations (PEMDAS). First, let's calculate the cube of (1/10,000):
(1/10,000)^3 = 1 / (10,000)^3
Now, let's simplify the denominator:
(10,000)^3 = 1,000,000,000,000
So, our expression becomes:
(1 / 1,000,000,000,000)^(1/4)
Taking the Fourth Root
To take the fourth root of a number, we can raise it to the power of 1/4. In this case, we get:
((1 / 1,000,000,000,000)^(1/4) = (1 / 1000)
Simplifying further, we get:
(1 / 1000) = 0.001
The Final Answer
Therefore, (1/10,000)^(3/4) = 0.001.
I hope this article has helped you understand how to raise a fraction to a fractional power. Remember to follow the order of operations and simplify your expressions carefully to get the correct answer.
