In Exercises 39–54, rewrite each expression with a positive ratio...

Question

In Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible.

16^-¾

Accepted Answer

Welcome back. I am so glad you're here. We're asked to simplify the following expression. We're given 36 raised to the negative three halves. Our answer choices are answer choice. A negative 36 answer choice, B one 216th, answer choice C 72 answer choice D one 36th. All right. The first thing we notice here for simplifying is that this 36 is being raised to a negative exponent. Exponents do not like being negative. They want us to get rid of the negative. How do we do that? Well, whenever something's in the numerator and being raised to a negative exponent, it needs to get to the denominator. And whenever something's in the denominator being raised to a negative exponent, it needs to get to the numerator. This 36 raised to the negative three halves is essentially in an unwritten numerator. So it needs to get down to the denominator as it does. So the new numerator becomes just one and that's divided by we bring down this 36 raise to them. But now that it has moved to the denominator, it is no longer a negative. It is a positive 3/2, we still have some more simplifying to do. We can simplify this 36 raise to the 3/2. We recall from previous lessons that what is in the denominator of our rational exponent. So in this case, two, that's the root that we are taking here. So we can set this equal to one divided by. And now we're taking the square root of 36 and we recall that what's in the numerator of our rational exponent. So in this case, a three, that is what this is being raised to. So we have the squared of 36 cubed in our denominator. Well, we can simplify the square root of 36. That's 6. So we have one divided by six cubed and now we can simplify six cubed, six cubed is 216. So this whole thing is one, 216th. We look at our answer choices and this matches with answer choice B well done. We'll catch you on the next one.

In Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 16^-¾

Key Concepts

Negative Exponents

Rational Exponents

Simplification of Exponents

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