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# Simplifying hairy expression with fractional exponents

Sal simplifies hairy expressions with rational exponents. For example, he simplifies (125^-⅛*125^⅝)/(5^½) as 5.

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• Can someone help me? How did (3w^2)^-2/3 * (3w^2)^-5/6 turned into (3w^2)^-3/2??
• When multiplying, exponents get added. For example: `X^2 * X^3 = X^5`.
Your problem is very similar, but we have to add fractions. So, we need a common denominator (LCD = 6).
Add the exponent: `-2/3 * 2/2 - 5/6 = -4/6 - 5/6 = -9/6`
Then reduce the fraction: `-9/6 = -3/2`
So that is how `(3w^ 2)^-2/3 * (3w^2)^-5/6` became `(3w^2)^-3/2`
Hope this helps.
• At , shouldn't the w in the answer be in the denominator? making the answer:
1/(8w^15/2)

but then you'd have to separate the 15/2 to get it out of the denominator?
• i personally don't think you can simplify them that way,and you need to have a common denominator,they and all numbers are basically having 1 as a denominator and are fractions of 1.. it can't go the other way around without changing the expression. but it can work since it's multiplication
• why can't u cancel 1/2 by 1/2 if its in fractions .
• The 1/2's are exponents, not base numbers. Division divides bases to cancel things out. We don't cancel out exponents and leave the bases.

Also, notice the bases of the exponents are different.
If the problem was 5^(1/2)/5^(1/2), then the bases match and the exponents match so the numbers are equal and you can divide them and get 1. But the problem in the video is 125^(1/2)/5^(1/2). These are not the same number. So, you need to use properties of exponents to convert to a common base. Or, as Sal shows in the video, we can rewrite the problem has one fraction raised to the common exponent. This then lets him reduce the fraction.

Hope this helps.
• At pm How would i simplify sqrt(n)/sqrt(n+1) ? (This is just part of a problem that has to do with power series..)
• At , why is 4^(-3/2) equal to 1/8?
• ok, so first thing, it's basically 4^3 * 4^1/2(or radical of 4). 4 at the third power is 64, all that is a radical,therefore radical of 64 is 8
• At , he makes the entire fraction to the power of 1/2. Can't I just apply the second property and subtract 1/2 from 1/2 in the numerator in denominator?
• No, you need a common base to divide by subtract exponents. 125 does not equal 5, so there is no common base. You could change 125 into 5^3 to get a common base.
[5^3]^(1/2) / 5^(1/2)
Simplify the numerator by multiplying exponents.
5^(3/2) / 5^(1/2)
Now, you can subtract exponents to do the division. And, you get 5^(2/2) = 5^1 = 5

Hope this helps.
• hi how are you guys doing
• None of these videos are helping me. I am doing a math book that gave me a question like this one:
* (0.3x^-1)^3 (3xy^-2)^2 *
These question make no sense to me and there is nothing on Khan that explains it (or if there is, I haven't found it). If you have anything to help me, please do!
• If a and b are positive constants,simplify (ab√ab)/(∛(a^4 ) ∜(b^3 )).