Simplify each exponential expression in Exercises 23–64. (4x^3)^−...

Question

Simplify each exponential expression in Exercises 23–64. (4x^3)^−2

Accepted Answer

So this problem it says consider the given exponential expression. Seven A. To the fifth. All that to the negative third. And we want to simplify so let's go ahead and look at our expression. So we have 7.8 to the fifth. So the negative 3rd power. So if you notice here we have an exponent raised to an exponent and a number raised to an exponent. We have an exponent raised to an exponent. We're gonna multiply the exponents together. So kind of example if I wrote a to the M. Race at the end this would be the same thing as saying a the M. Times it. So this is an exponential role we should remember from our lesson but we'll go ahead and solve our exponential. So we're gonna kind of distribute this exponential to both the seven and the eight to the fifth because the seven also has to be taken into account. So let's go ahead and split this up. You have seven. The exponential is the native 3rd And we have 8 to the 5th. Which also multiply By -3 based on our role starting go ahead and simplify this. Now we have a negative exponent and we'll have it in both of our terms here. Actually we have a negative exponents wherever other rules is that we can rewrite it as a fraction with a positive exponent. So for your seven to native third. How can we write this with a one on the top and seven to the power of positive third on the bottom a naked expanded just kind of turns into a fraction. So let's look at R. A. Now. Well we can a. to the negative 15 which means based on this one over seventh. The third times one over A. To the 15 by our exponential rule. Finally we can go ahead and simplify even further. We have 1/7 to the third which in the calculator, this is 343 Multiplied by 1/8 - 15. When we do that We get one over 343 A. to the power of 15. So this is our simplification of our problem which means our answer is answer. A. Alright I hope to help you solve the problem. Thank you for watching. Goodbye.

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