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.

The sixth root of g to theįifth is the same thing as g to the 5/6 power. 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 So, the sixth root of g to the fifth, is the same thing as g to the fifth, raised to the 1/6 power. 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'. An ability to work well with exponents of all types is an advantage in calculus where derivatives can be made simpler via the 'power rule.It really depends how creative and curious a mind you are.The problems at this level tend to be a straight radical with no additional powers mixed in, although there is a possibility of needing to find the reciprocal of the answer.Negative exponents mean to reciprocate (or find the inverse/opposite), and a fraction like 1 n root.Knowledge of the exponent rules, including negative and fraction values, is sufficient to perform the exercise accurately and efficiently. The student is asked to find the expression(s) (if any) that are equivalent the original and select it from the multiple choice list below. Determine the equivalent expression(s): This problem has a numerical expression involving a rational exponent with fractions.

The student is asked to find the value of one of the variables and type it in the text box below. Find the value of the variable: This problem has a numerical expression involving a rational exponent with fractions and variables.There are two types of problem in this exercise: This exercise practices evaluating numerical expressions with rational exponents, and convert between equivalent forms of exponential and radical expressions. The Rational exponents and radicals exercise appears under the Algebra I Math Mission.