Fractional powers of indices

A fractional power of an index signifies the index raised to an exponent that’s not equal to 1. To understand this concept better, let’s take a look at an example from trigonometry. Say we want to find an angle whose sine equals 0.5. We know that in trigonometry, sin(x) = x for all values of x, so this should be easy, right? Let’s try it and see if we get the correct answer!

For today’s lesson, we will be discussing fractional powers of indices, or, as they are sometimes called, index powers. Indices are mathematical things that stand in front of variables and represent some quantity of them; an example would be to say that formula_1 represents the first power of the index 3, or that formula_2 represents the second power of the index 1, etc. Now, what does this have to do with fractional powers?

The Basic Definition-Fractional powers of indices

So, what are the fractional powers of indices? It’s pretty simple: with indices, you don’t multiply; you raise to a power. This may seem strange since multiplying is normally equal to raising something to power in mathematics—but it makes sense when you think about matrices or tensors which usually represent objects that have different numbers of spatial dimensions. However, fractions still work in physics and are used as shorthand for other mathematical expressions; for example, Einstein’s famous equation E=mc2 gets closer to its full form when you write it as E=(mc)^2. This lets us combine concepts from both multiplication and powers of indices into one process that we can use for simplifying certain mathematical expressions.

An Example Problem-Fractional powers of indices

Let’s take a look at an example problem to better understand how you can use fractional powers of indices. The problem below asks you to find what third-order term is represented by ab. Step 1: Plugin values for our variables in terms of and find A and B. A = 1 and B = 4 Therefore,  = ab. To solve for abwe plug those values into the equation above and solve for (1)(4) which equals 4 in absolute value. Therefore, (1)(4) represents the third-order term ab. So, in full sentence form: Third-order term Ab represents (1)(4).

Fractional Powers In Maths

What Is It? A fractional power is just like a regular power, except instead of it being to an exponent, it is to another fractional power. Here’s an example: 0^1/3 = 1 (i.e., 0^0/3 = 1), and 1/4 = 0^1/2. Why Bother? Honestly, I’m not 100% sure why anyone would want to do such things. There are certainly some valid applications of fractional powers in maths (like working with compound interest problems where money compounds on itself), but most people probably won’t ever use them in everyday life.

Indices Fractional Powers

Indic fractional powers is an uncommon but crucial concept. More often than not, when students first encounter fractional indices, they are told that fractional powers are bad. This should never be taught because it creates an association between math and guilt. It also makes them lose confidence in their ability to solve these problems later on in life. How do you think you’d feel if someone told you that fractions were bad? As with many other mathematical concepts, fractional powers need to be introduced slowly and given time to marinate in our brains before we can start building upon previous knowledge.

Bonus – Why Does This Work?

Remember, to calculate an index, we square root of √[n]. That’s it. We have our index! The same thing applies here; we are just multiplying and dividing by a constant value. This will alter our expression slightly from its original form, but in its simplest form, that’s all there is to it. Fractional powers of indices always work because when you multiply and divide any rational exponent by another rational exponent, you end up with another rational exponent.

Conclusion

Indices can be fractional powers, which means that the index used can be greater than 1 or less than 1. When an index is used as a fractional power, it increases or decreases the corresponding power of the variable by a specified amount. For example, if you want to square the variable x to three decimal places instead of two, you could multiply your original formula with this power (x^2) by 2x^0.3 instead of just x^2. Check out this post to learn more about how to use indices as fractional powers!