![]() You applied what you know about fractional exponents, negative exponents, and the rules of exponents to simplify the expression. And then, if you multiply these exponents, you get what we have right over there.\( \newcommand\) Another way of thinking about it is you could view this as, you could view it as, x to the 1/7 to the negative one power. Same thing as raising it to the negative of that exponent. You're taking the reciprocal of something, that's the And so, d must be equal to, d must be equal to negative 1/7. And so, that is going toīe equal to x to the d. So, that is the same thing as x to the negative 1/7 power. Something to a power, that's the same thing as that something raised to the negative of that power. This is the same thing as one over, instead of writing the seventh root of x, I'll write x to the 1/7 power is equal to x to the d. Well, here, let's just start rewriting the root as an exponent. or pauseįor this question as well and see if you can work it out. You in the last one, but pause this video as What is the value of d? Alright, this is interesting. True for x greater than zero, and d is a constant. We can also have rational exponents with numerators other than 1. If the index n n is even, then a a cannot be negative. We can use rational (fractional) exponents. The sixth root of g to theįifth is the same thing as g to the 5/6 power. Radical expressions can also be written without using the radical symbol. So, that's the same thing as g to the 5/6 power. To another exponent, I can just multiply the exponents. I raise something to an exponent and then raise that whole thing Saw in the last example, that's the same thing as g Let’s assume we are now not limited to whole numbers. The Power Property for Exponents says that (a m) n a m n (a m) n a m n when m and n are whole numbers. ![]() When we use rational exponents, we can apply the properties of exponents to simplify expressions. So, the sixth root of g to the fifth, is the same thing as g to the fifth, raised to the 1/6 power. Rational exponents are another way of writing expressions with radicals. Sixth root of something, that's the same thing as What is the value of d? Well, if I'm taking the The following equation is true for g greater than or equal to Or similar types of problems dealing with roots andįractional exponents. So, this is not going toīe equivalent for all v's, all v's for which thisĮxpression is defined. So, that is the same thingĪs v to the 7/3 power, which is clearly different So, that's the same thingĪs v to the 1/3 power, and then, that to the seventh power. actually, no, this wasn't theĬube root of v to the seventh, this was the cube root of v,Īnd that to the seventh power. Is this going to be equivalent? Well, one way to think about it, this is going to be the same thing as v to the 1/3 power. This is the cube root of v to the seventh. ![]() That's what we have right over here, so that one is definitely equivalent. We have right over here, so that is equivalent. So, v to the third to the 1/7 power, well, that was the form that So, this is going to be the same thing as v to the three times 1/7 power, which, of course, is 3/7. Then, that's the same thing as raising it to the product And if I raise something toĪn exponent and then raise that to an exponent, well To v to the third power, raised to the 1/7 power. Something is the same thing as raising it to the 1/7 power. V to the third power, v to the third power, the seventh root of Out if things are equivalent is to just try to get These are equivalent to the seventh root of v to the third power. Video and see if you can figure out which of We're asked to determine whether each expression is equivalent to the seventh root of v to the third power. Eventually, you will begin to see Algebra in places that you wouldn't have if you weren't looking for it. So my advice to you: think of every skill you learn as an opportunity, not a chore. In fact, many times great things are discovered when you take what you learn from one skillset and apply it to another skillset. However, as I become smarter I will be able to take what I have learned elsewhere and apply it to other skills. Now it is true that not all of these tools will help me make money-at least not directly. Whether it is programming, computer science, physics, chemistry, engineering, etc, the skills learned in Algebra can come in very handy. When I was young, I put in the hard work to learn Algebra, and now I use it all over the place. ![]() They say that since they will never be an engineer or scientists, they shouldn't have to learn it.īut instead of thinking of it that way, think of the opportunities you could give yourself. People often complain about learning math and "how will it be useful". It really depends how creative and curious a mind you are. ![]()
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