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Simplify each expression using the addition or subtraction rules of exponents. Assume that a, b, m, and n represent positive integers.$$ rac{w^{5 n+3}}{w^{2 n}}$$...

Question

Simplify each expression using the addition or subtraction rules of exponents. Assume that a, b, m, and n represent positive integers.$$ rac{w^{5 n+3}}{w^{2 n}}$$

Simplify each expression using the addition or subtraction rules of exponents. Assume that a, b, m, and n represent positive integers. $$ \frac{w^{5 n+3}}{w^{2 n}} $$



Answers

Simplify each expression, writing the answer as a single term without negative exponents.
$$\left(\frac{m}{3}\right)^{-1}+\left(\frac{n}{2}\right)^{-2}$$

Okay, so let's never be writing quite negative exponents as a positive one. So he gets three over em, plus two squared. That's for over and thread. And I will multiply, decided by am over and in this one by and squared over and squared. Since we want to combine this into a single fraction. So we have three and squared what's for em over and squared times up.

Our first step is to make all of the negative exponents positive that has an exponent of ones that will stay where it is. But everything else will will switch from numerator to denominator or vice versa. So in the numerator I'll have five squared, an end to the fifth and the denominator. I'll have to to the positive third and the positive fourth, etcetera. And the original end of the first is going to stay. They're five squared is 25 me do down here is 25 to Cube is eight. How? Subtract my exponents for the EMS. I have more in the numerator sets and of the first I don't need to write the M or the first and my ends. I will add those exponents and that will be in the denominator.

Let's go ahead and leave the six on the bottom and we'll go ahead and divide the EMS. Now to do that, we subtract the powers three minus one is to the second power. We write that on the top in the numerator. We also divide the ends by subtracting the exporters again. So to minus the 11 on the bottom is negative. Nine. So put that one on the top is well, now we gotta move this end of the negative nine to the bottom to make it a positive exponents to leave the m squared up top the six in the bottom and in the end, to the positive night.

We need to simplify the following expression using the rules of exponents. When we have base raised to a power raised to another power, we multiply the exponents. So this simplifies to x raised to the two times empower and that is our final answer.


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