In Exercises 55–78, use properties of rational exponents to simpl...

Question

In Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers.3^½ ⋅ 3^¾3^¼

Accepted Answer

Welcome back. I am so glad you're here. We're asked to simplify the following expression by using the properties of rational exponents. The expression we're given is in the numerator, we have 17 raised to the one third multiplied by 17, raised to the 5/6. And that is all divided by, in the denominator, we have 17 raised to the 1/6. Our answer choices are answer choice. A 17 raised to the two thirds answer choice. B one answer choice C 17 raised to the 1/9 and answer choice D 17. All right, we recall from previous lessons that when we have like bases. So the bases here are all 17, they're all alike. When we are multiplying those bases, we are going to add their exponents. So in the numerator, we're taking 17 raise to the one third, multiplied by 17 rays to the 5/6. So we can take one third plus 5/6. And in order to add fractions, they need to have a common denominator which in this case will be six. So we'll multiply 1/3 by two halves and multiplying two and one gives us two that's divided by multiplying two and three gives us six. So we have 2/6 plus 5/6 and we can add straight across our numerators. Two plus five is seven and our denominator remains six. So in the numerator of our original expression, we have 17 raised to the new exponent is 7/6 and that is divided by 17, raised to the 1/6. We recall from previous lessons that when we have these like bases, which we still do and they are being divided, we are going to subtract their exponents. So this time, we will take 7/6 minus 1/6. This time we do have common denominators. So we can go ahead and subtract our numerators seven minus one equals six. So we have 6/6 which simplifies to one. So we now have 17 raised to the first power which is just 17. So this all simplifies to 17. We look at our answer choices and that matches with answer choice. D well done. We'll catch you on the next one.

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In Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers.3^½ ⋅ 3^¾3^¼

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