Simplify.(x4y)3\left(\frac{x}{4y}\right)^3

x364y3\frac{$$x^3$$}{$$64y^3$$}

Simplify. ( x 4 y ) 3 \left(\frac{x}{4y}\right)^3

So let's take a look at this next practice problem here. We have our quotient x divided by four y all raised to the third power. So like other problems that we've seen before, we're gonna use our power of a quotient rule, sometimes also known as the quotient to a power property, really the same thing to solve this. So the basic idea, remember, is you're gonna take the exponent of three and you have to distribute it to everything that's inside of the parentheses in the numerator and denominator. So you distribute the x the three to the x and the exponent of three also to the denominator of four y. And then we simplify. So what we're gonna do here is we're gonna raise x to the third power. We can't really do anything with that numerator anymore. We can't simplify it. But on the bottom, we're gonna distribute this three to not only just the four, but also the y as well. So the best way to do this is to maintain the parentheses and keep it there. So we have four y raised to the third power. Because now we can see we're actually gonna have to reuse another rule to simplify this further. So sometimes you can have a power of a quotient rule that kind of will lead to a power of a product rule. In the denominator, we have this whole expression four y that's raised to the third power. That power over product rule tells us we have to distribute this three exponent to the four and also the y. So lots of problems will have you use multiple rules to simplify these expressions, and this is one of them. So on the numerator, we just don't change anything. This is still just x to the third power. We can't simplify this any further. But on the bottom, once we distribute the x one to the three to the four, you're gonna get four to the third times y to the third. You can keep that parentheses or that multiplication symbol in there or you can basically just rewrite them both with their own parentheses, either way. So what we do here is we ask ourselves, is this fully simplified? Well, with for when you take expressions like, that involve variables to exponents like x to the third and y to the third, you can't simplify those any further. But with this four to the third power, you can because four to the third power actually is a number. So, typically, when you simplify, numbers raised to exponents have to be sort of converted into the most simple forms without any exponents. And And so all we have to do for this last step is we just have to figure out what four to the third power is. So four to the third is basically just four times four times four. Four times four is sixteen, and sixteen times four is 64. So you can go ahead and work that out on the side, but this basically just equals 64. And so I'm just gonna write 64 y to the third power. Now I have all my all of my numbers raised to exponents have been simplified, and I can't do anything with the x to the third and the y to the third. So this actually is the most simplified form that I can write this expression is in, and that's the right answer. Alright? So again, multiple rules can sometimes be used in the same problem in order to simplify expressions. Thanks for watching. Hope this helped, and, we'll see you in the next one.

Simplify.(x4y)3\left(\frac{x}{4y}\$$right)^3$$

x364y3\frac{$$x^3$$}{$$64y^3$$}

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5. The Real Number System

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Liberal Arts Math

5. The Real Number System

Power Rules

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Simplify.
$open paren x over 4 y close paren cubed$

$the fraction with numerator x cubed and denominator 64 y$

$the fraction with numerator x cubed and denominator 4 y$

$the fraction with numerator x cubed and denominator 4 y cubed$

$the fraction with numerator x cubed and denominator 64 y cubed$

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Simplify.(x4y)3\(\left\)(\(\frac{x}{4y}\)\(\right\))^3

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Simplify.
$open paren x over 4 y close paren cubed$