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# Rewriting roots as rational exponents

Sal solves several problems about the equivalence of expressions with roots and rational exponents. For example, rewrite ⁶√(g⁵) as g^⅚.

## Want to join the conversation?

• When am I going to use this math in life? This is a serious question.
• Well, what profession are you considering?

Even if you're interested in something like painting, where math isn't that involved, an understanding of exponents is vastly helpful in managing money, savings, interest rates, investments, etc., which everyone certainly has to deal with at some point. Hope that I helped.
• A constant is a number which doesn't change, unlike a variable, which can change, i.e. d at has only one value, while x can have any value greater than zero for the equation to be true.
• Someone give me an example of how I'm gonna use in life...
• Howdy EhP,

It really depends how creative and curious a mind you are. People often complain about learning math and "how will it be useful". They say that since they will never be an engineer or scientists, they shouldn't have to learn it.

But instead of thinking of it that way, think of the opportunities you could give yourself. When I was young, I put in the hard work to learn Algebra, and now I use it all over the place. Whether it is programming, computer science, physics, chemistry, engineering, etc, the skills learned in Algebra can come in very handy. Now it is true that not all of these tools will help me make money--at least not directly. However, as I become smarter I will be able to take what I have learned elsewhere and apply it to other skills. In fact, many times great things are discovered when you take what you learn from one skillset and apply it to another skillset.

So my advice to you: think of every skill you learn as an opportunity, not a chore. Eventually, you will begin to see Algebra in places that you wouldn't have if you weren't looking for it.

Learn on, my friend.
• At about 0.50, why do you multiply the two numbers for v to the 3rd to the 1/7? I kind of get it, but I'm still a little confused. Wouldn't it be v to the 3 1/7?
• The properties of exponents specify that when one exponent is raised to another exponent, you multiply the exponents. for example: (x^2)^3 = x^(2*3) = x^6.

So, in the video, Sal has (v^3)^(1/7). Multiply the exponents: v^(3/1 * 1/7) = v^(3/7)

Hope this helps.
• how do you rewrite the root if its a negitive decimal with a fraction as an exponent?
• FIrst off, we cannot have a negative on any of our even roots (square, 4th, 6th, etc.) without getting into imaginary numbers. So if you are asking (-.5)^(1/5) we could write the square root sign with a raised 5 on the crook of the root sign, and a -.5 inside.
Hope this helps.
• How does work, when x has a positive exponent, turn into a negative?
I understand that x^-2 is the same as 1/x... though I dont understand how that works either, it's just memorised.
• But what if there is more than one square root on the base? For example, log a^1/2^a^2.
• what if you were trying to find 32 to the power of 3/2? What would you do then
• 1) Change to a radical: 32^(3/2) = [ sqrt(32) ]^3
2) Simplify the radical by finding and taking the square root of all perfect square factors:
[ sqrt(32) ]^3= [ sqrt(16) * sqrt(2) ]^3 = [ 4 sqrt(2) ]^3
3) Apply the exponent & simplify:
[ 4 sqrt(2) ]^3 = 4^3 * sqrt(2)^3 = 64 sqrt(8)
64 sqrt(8) = 64 sqrt(4) sqrt(2) = 64 * 2 sqrt(2) = 128 sqrt(2)

Hope this helps!