Simplify each exponential expression in Exercises 23–64.

Question

{(\frac{3 x^{4}}{y})}^{- 3}

Accepted Answer

Hi there. This problem says consider the given exponential expression two K to the fifth divided by M to the negative fourth overall. And simplify the expression. So let's take a look at our expression, we have to cater to the five Over M two Native 4. So I'm gonna go ahead and write this here To the 5th over em To the -4 to to simplify this. So if you notice here we have the exponents on the outside at the top and we have exponents inside the fraction. I'm first gonna rewrite this in exponential expression. So if you look here, we have an M on the bottom. If you have a variable on the bottom of a fraction, we can instead rewrite this five instead of them being on the bottom, we can write this as M the negative one on the top. So that's something we should remember about exponents. But if you have an excellent and a fraction on the bottom will turn into a negative exponent on the top of the fraction and vice versa. Some write that as this to the night of the 4th. No, We're taking all of our excellence and variables to the negative 4th power. When we take an exponent to a power we're going to multiply these two exponents together. So let's go ahead and split up this equation we have here. I have R2, We'll put that to the -4, we're gonna distribute this negative four to every one of these variables in constance. So okay, it's the fifth two times a day before nm Native one And state of four. So as I mentioned before when you're raising exponents exponents. You just multiply the exponents together. So over here we get two to the -4 which I'll evaluate in a second. We have K5 times negative four. This gives us K. It's the negative 20 and here we have em date of one times the rate of four that gives us em. So the fourth. Now I wanna look at this to the -4. Remember what I mentioned before? It's that a negative exponent will move it to the other part of the fraction and change the exponent to positive. So this is one of our expanded roles. But if I have to the native four I can instead write this as one over to the power for. So we're changing into a fraction With a positive exponents and the denominator similarly to what we did with the M 2 -1. Now we can go ahead and evaluate all of this. One over. Two to the fourth or you know, two to the fourth is 16. Number 16 We have caves that negative 20. So we can also put decay to the 20 on the bottom And this is multiplied by M to the 4th. We simplify all this. We can multiply it over. We get one times one times into the fourth, says into the 4th divided by K to the 20th. So that is our answer. Our answer is answer. C Okay, I hope to help you solve the problem. Thank you for watching Goodbye.

Simplify each exponential expression in Exercises 23–64. ${(\frac{3 x^{4}}{y})}^{- 3}$

Key Concepts

Negative Exponents

Power of a Quotient Rule

Power of a Product Rule

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