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Destinyyyy
 one year ago
Can someone explain this to me?
Destinyyyy
 one year ago
Can someone explain this to me?

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Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.1Simplify the following expression. Express the answer w/positive exponents (3xy^1/y^3) ^4

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.1= (3x/ y^1 y^3) ^4 = (3x/y^2) ^4 (3x/y^2) ^4 = (3x)^4/(y^2)^4 = 3^4 x^4/y^8 = y^8/81x^4

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.1I know that my answer is wrong.. Where did I mess up?

phi
 one year ago
Best ResponseYou've already chosen the best response.1it's not clear what the starting expression is. \[ \left(\frac{3xy^{1}}{y^3}\right)^{4} \]?

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.1Yes thats correct.. Sorry I dont get how to use the equation thing.

phi
 one year ago
Best ResponseYou've already chosen the best response.1ok so the y's inside the parens can be handled a few ways. one way: write y^1 as 1/y \[ \left(\frac{3x}{y \cdot y^3}\right)^{4} \\ \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1the other way: y^1 / y^3 . keep the base y. new exponent is top minus bottom exponents: 1  3 = 4. so y^4 \[ \left(3xy^{4}\right)^{4} \\ =\left(\frac{3x}{y^4}\right)^{4} \\\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1I would "flip" the fraction and change the sign of the 4 exponent to +4 \[ \left(\frac{y^4}{3x}\right)^{4} \]

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.1Um I think so... Give me a second

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.1I have y^16/ 3^4 x^4 = y^16/?

Destinyyyy
 one year ago
Best ResponseYou've already chosen the best response.1I know the final answer is y^16/(3x)^4 but im stuck on the last part

phi
 one year ago
Best ResponseYou've already chosen the best response.1if you start with \[ \left(\frac{y^4}{3x}\right)^{4} \] all the exponents stay positive

phi
 one year ago
Best ResponseYou've already chosen the best response.1if we do it "brute force" remember that \[ \left(\frac{y^4}{3x}\right)^{4} = \left(\frac{y^4}{3x}\right) \left(\frac{y^4}{3x}\right) \left(\frac{y^4}{3x}\right) \left(\frac{y^4}{3x}\right)\]

phi
 one year ago
Best ResponseYou've already chosen the best response.1and when you multiply fractions, you multiply top times top y^4 * y^4 * y^4 *y^4 = y^16 (the short way is to use the rule \[ (a^b)^c= a^{b\cdot c} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1and the bottom is \[ \left( 3x\right)^4 \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1or 3^4 * x^4 or 81x^4 there are a few ways to write it.

phi
 one year ago
Best ResponseYou've already chosen the best response.1btw, when you started *** Simplify the following expression. Express the answer w/positive exponents (3xy^1/y^3) ^4 **** on the next post you say = (3x/ y^1 y^3) ^4 = (3x/y^2) ^4 notice you changed 3xy^1 to 3x/y^1 when you do that (move y^1 from the "top" to the "bottom"), you should change the sign of the exponent. you should have written: = (3x/ y^1 y^3) ^4 and then you get = (3x/y^4) ^4 and now you will get the correct answer

phi
 one year ago
Best ResponseYou've already chosen the best response.1and to complete the thought... the other way to do this is \[ \left(\frac{y^4}{3x}\right)^{4}= \frac{\left( y^4\right)^4}{\left( 3x\right)^4}\] and then simplify the top using the rule \[ (a^b)^c= a^{bc} \] to get \(y^{4\cdot 4} = y^{16}\)
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