Simplify each exponential expression in Exercises 23–64. 10x^4 y^...

Question

Simplify each exponential expression in Exercises 23–64. 10x^4 y^9/30x^12 y^−3

Accepted Answer

Hi there. So this problem it says consider the given exponential expression negative 16 X. To the ninth times Y to the eighth divided by four X. To the fifth times Y to the first. Everyone is simplify this expression. So let's go ahead and take a look at this. I'm going to rewrite this as native 16. Thanks to the Knights. Why? into the 8th over four X. The fifth. Why to the first? Since the vision hours? We write it as a fraction. Now we're gonna divide all these expressions. So if you kind of look here, we can kind of match up exactly what we needed to fight. So like our to this we have our 16 are negative four. We have our X. To nine X. To the fifth and we have our Y to the eighth. Ry to the first. So let's go ahead and split these up. So we have a native 16 over a four. Then we have and extra nights over X to the fifth. And finally we have a Y. To the eighth over wide to the first. So we're gonna go ahead and divide all of these separately. So the first one is easy. We have negative 16/4 which is just negative four. Now let's take a look at the extra ninth over the X. Of the fifth. So we're actually divided two exponents. We divide two exponents. We're actually going to subtract our exponents. So let's say I had an exponent X. To the M over X to the N. This is the same thing as saying X to the m minus. in this is one of our exponent rules we should know from our lesson. So we have X. In the night Divided by X to the 5th. So by our exponent rule It's the 9 -5. The same thing for away We have Y. It's a pair of 8 -1. Now we can simplify. We haven't taken four X. 2 9 -5 X. to the 4th. And why the 8 -1 is why to the seven. So this will be our final answer negative. Four X to the fourth, Y. To the seventh which is answer C. Okay I hope to help you solve the problem. Thank you for watching. Goodbye.

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