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

Question

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (p^1/5p^7/10p^1/2)/(p^3)^-1/5

Accepted Answer

Welcome back. I am so glad you're here. We are given this expression in the numerator we have B to the one third times B to the 1/5 times B to the 15 months. And that is all over in our denominator. We have B squared raised to the negative 15 months. And there are so many ways to simplify this. You might have started somewhere completely different from where I'm going to start, which is fine. There are lots of ways to do this. But I'm going to start in the denominator. Excuse me. And we look and we see we have a power being raised to a power. And we recall from previous lessons on power rules that when we have a power raised to a power we are going to multiply those. So we're going to take two times negative 7/15. So two times negative 7/15 says negative 14 15 months. So when the denominator are new exponents is be raised to the negative 14 15th. And in the numerator we still have B to the one third times B to the 1/ times B to the 8 15 months. So next I am going to look at this denominator and we see that there's a negative exponent here. Whenever we see a negative exponent that is telling us you're on the wrong side of the division line. So B to the negative 14 15th, you need to get up to the numerator. And when you do your negative in the exponent will disappear. So now this will read b to the one third times B to the 1/5 times B to the 8/15 times B to the positive. 14 15th. Now they are much happier with their positive exponents. Right now the next power rule that I'm going to recall is when we have the same base being multiplied, we are going to add the exponents together so we're going to take one third plus 1/5 plus 8/15 plus 14 15th. We need to have a common denominator to add fractions together. The common denominator will be 15. So we multiply one third times 5/5 to get a denominator 15 and we'll multiply 1/5 times three thirds to get a denominator of 15. So now this will read five times one is 15 so 50. Excuse me? Five times one is five, so 5/15 plus three times one is three, so 3/15 plus 8, 15 plus 14 15 months. So now we have a common denominator, we can add our enumerators, five plus three is +88 plus eight is and 16 plus 14 is 30. So our new numerator is 30/15. We can simplify that. 30 divided by 15 equals two. So our new exponents is too, we have B squared. Now we need to make sure that we are writing our answer without negative exponents, two is positive. So this works. We look at our answer choices and this matches with answer choice. A. Well done. We'll catch you on the next one.

Simplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (p^1/5p^7/10p^1/2)/(p^3)^-1/5

Key Concepts

Exponent Rules

Negative Exponents

Simplifying Rational Expressions

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