Calculate each value mentally. (20^2/3)/(5^3/2)

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Hello. Everyone in this video we're going to be looking at this practice problem where we want to compute the value of 1 53 to the three halfs power divided by 17 to the three halfs Power cognitively. So without a calculator. So whenever you're trying to simplify problems without a calculator, you want to try to break it down and make smaller numbers to make it easier to compute. So in this case you can see that we're working with 153 and 17. Well if we think of the factors of 153, we can do 17 times nine. So I want to try to get the fraction Divided by 17 alone so that I can rewrite it as nine because 9 is a smaller and easier number to work with without a calculator. So If I want to go from the original expression to this fraction you can see that both my numerator and my denominator or 153 and 17 have the same exponent of three divided by two. So because they have the same exponents, I can pull it out and put it on the outside of the parentheses. And if I pull it out you can see it's the same thing because when I have an exponent on the outside of the parentheses, I need to multiply that to each component inside the parentheses. So I would still need to multiply it to the 17 and the 153. So I can go back and forth between these expressions but now I have 153 divided by 17 alone. So I can rewrite this as nine because 153 divided by 17 is nine. Again with this exponent on the outside of three divided by two. But now when we think of writing nine As an exponent we have three times three. So this is the same as three squared. So if I plug in three squared for nine This equals three squared With the three divided by two exponents on the outside. And because I have the exponent on the outside of the parentheses, I need to multiply it to the exponent on the inside. Which in this case is to So this expression becomes three To the power of two times 3/2ves or 3 to the power of six divided by two and six divided by two is 3. So this becomes three To the 3rd power. Well that's something I can do. So if I do three times three times three I have nine times 3 which is equal to 27. So now I solved this complicated expression down to 27 by breaking it down and working with the smaller numbers. So 27 becomes my final answer when I evaluate this expression and you can see that that aligns with answer choice C. So hopefully this video helped and see you next time

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Calculate each value mentally. (20^2/3)/(5^3/2)

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