Question 72862: SIMPLIFY
1. 5x^3/(5x)^3
2. (7t^3/21t)^3
3. (2k^3/3k^-2)^-2
Answer by jmg(22)   (Show Source):
You can put this solution on YOUR website! 1. Solve the bottom first so that you have 5x^3/125x^3. Then you just cancel out the x^3 and simplify 5/125 to 1/25.
2. Simplify inside the parentheses first. 7/21 would reduce to 1/3. The t on the bottom will cancel out with one on the top and leave you with
(t^2/3)^3. Then raise everything to the 3rd power. (t^2)^3 = t^6, 3^3= 27.
Giving the solution t^6/27
3. you cannot reduce 2/3 so you solve the k. When the variables are being divided you subtract the exponents. So 3 - (- 2) = 5
So you get (2k^5/3)^-2. When the exponent is negative you flip the fraction and change the exponent to a positive (you also could have done this in the previous step with the k^-2, but I thought it was easier to explain this way)
So you have (3/2k^5)^2
Square everything in the fraction.
9/4k^10
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