5

Simplify and write the answer with positive exponents only.a) 𝑥 ^ 5 * 𝑥 6 ^ bd) 𝑥 ^ 9 / 𝑥^ 4e) 𝑥^ 9/ 𝑥^−4f) f...

Question

Simplify and write the answer with positive exponents only.a) 𝑥 ^ 5 * 𝑥 6 ^ bd) 𝑥 ^ 9 / 𝑥^ 4e) 𝑥^ 9/ 𝑥^−4f) f) 𝑥^ −4/ 𝑥^−9j) (4𝑥 ^2 ) ^3 (2𝑦 ^−2 ) ^4k) ( 1/ 2 𝑚^−2 𝑛^3 ) ^ 3

Simplify and write the answer with positive exponents only. a) 𝑥 ^ 5 * 𝑥 6 ^ b d) 𝑥 ^ 9 / 𝑥^ 4 e) 𝑥^ 9/ 𝑥^−4 f) f) 𝑥^ −4/ 𝑥^−9 j) (4𝑥 ^2 ) ^3 (2𝑦 ^−2 ) ^4 k) ( 1/ 2 𝑚^−2 𝑛^3 ) ^ 3



Answers

Simplify each expression, and eliminate any negative exponents. $$ \begin{array}{lll}{\text { (a) } \frac{a^{9} a^{-2}}{a}} & {\text { (b) }\left(a^{2} a^{4}\right)^{3}} & {\text { (c) }\left(\frac{x}{2}\right)^{3}\left(5 x^{6}\right)}\end{array} $$

All you need to know to solve this equation is that anything to the power of zero is one. So your answer is simply one. It doesn't matter what's inside the bracket, because no matter what it is, it will always If its to the power zero, it will always be equal toe one.

The first thing we'll do here is multiplier exponents. So I look at the original problem. They just multiply those exponents on the top A negative times negative gives me a positive 12 negative times negative used me a positive and negative times. Negative gives me a positive, and that would be my final answer, since all the exponents or positive and none of the bases air the scene.

Our first step is to make all of the exponents positive. So the three would be a positive exponent in the denominator before would have a positive exponents in the numerator the same for the A's, the five in the denominator and the seven and the numerator. I'm just moving the negative exponents of moving the base and making the exponents positive. The beat of the six days where it is and the beat of the negative Third will move to the numerator. So I will add these exponents. I'll subtract those exponents and the coefficients. I'll just, um 24 squared is 16 three squared is nine and then I have mores in the numerator. So seven minus five would give me eight of a second and beat of the six times be to the third. As I said, I'm gonna add those exponents that would give me be to the night

And this a questions required to simplify the from a gig suppression. As you can see here, there are two power of the same base. Be under to pull of the same Basie. So it's combined them together. Huh? Now this would be equal toe. I just write down the constant at as ah they are, as I will do them later. Now, looking at the 1st 2 powers, which has the same based be the division off powers of the same base, I will subtract explosion. So by writing down b the power off the first explorers in the numerator minds, the export indeed own Terminator four. Now the same applies to the the division off the poor to Power's off the same Basie. I will serve drug exports as well. So see to the boat off three minus eight. Oh, and that's compute them. Six. Support off minus two will remain the same for now. And 54 off mine's three as well. Now beat apart off nine miles. Four is five multiplied by C for off three miles eight, which is minus five. Now I don't want thes exposed to exist in the solution and defiant answer so I have to eliminate them and turn them tow positive by changing the places off the there thes powers. In other words, taking this broken so six miles to was in the numerator will turn to the eliminator and what was in the dominator will become the numerator. So now this is five to borrow mine three. It was Indian denominator. Now it will be in the numerator. So it's 5 to 4 on. The experience will be composed of 543 over 60 butterflies to wasin the numerator. Now it will become indeed denominator sex war off the positive too. Now on seeing what my suave as well will become in the denominator and explained will be postive bit about off five. The export is already positive, so it will remain in the numerator. Now The final tiny step is to compute the constant powers. So 54 of three is 125. Divide by beat four or five over six point of two is 36 c the board or five. So this is Theseus. Lucien


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