Simplify each expression. Write answers without negative exponent...

Question

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. 16m^-5n^4/12m^2n^-3

Accepted Answer

Hey everyone in this problem by using the rules of exponents were asked to simplify the following expression and eliminate the negative exponents and the expression were given is 56 A. To the negative nine be cute divided by 16. 8 to the four B to the negative one. All right, so 56 8 to the negative nine be cute. Divided by 16 A. To the four B. To the negative world. Alright, so first thing okay let's deal with the coefficients. Get these constant numbers out in front. 56. Divided by 16. Okay we can notice that they're both divisible by eight. If we divide 56 by eight we're going to get seven and if we divide 16 by eight we're gonna get to Okay so we have 7/ for that coefficient in front. Okay and then what about these A. And B terms? Okay well let's recall the following rule and we have a quotient rule. If we have A. To the exponent M. And we divided by A. To the exponents end we can write this as A. To the exponents M minus n. Okay so when we're dividing and we have the same base we subtract the exponents. So that means that we're gonna have a to the exponent negative nine minus four. Okay we have negative nine. The exponent in the numerator and the exponent of four in the dominator. So we have negative nine minus four and then the same for B B to the exponent three minus negative one. Alright now that that's done. We just want to simplify. These exponents So we have 7/ A. to the exponent -9 -4 is -13. Once we have them in this form it's just a matter of regular addition and subtraction and B. We have three minus negative one. That's gonna be three plus one. Which gives us an exponent. Yeah. Alright so we've simplified, let's just remember the question is asking us to eliminate negative exponents. Okay so we have a negative exponent on the A. Here. How can we deal with that? Well let's recall for negative exponents. If we have a. To the exponent negative end we can write this as one over A. To the exponent. Okay so we move it to the denominator and it becomes a positive exponent. So let's do that. So if we move the A. To the 13 into the denominator. Okay the numerator we're gonna have seven B. To the exponent four. So we have seven B. To the exponent four. Okay and in the denominator we still have our two and then we're gonna have a. To the exponent 13. So that is our simplified expression we've removed the negative exponents. Okay so we have seven B. To the exponent four divided by two A. To the exponent 13. And that is going to correspond with answer D. That's it for this one. Thanks everyone for watching see you in the next video

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. 16m^-5n^4/12m^2n^-3

Key Concepts

Exponents and Negative Exponents

Simplifying Rational Expressions

Combining Like Terms

Watch next