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.

49^-½

Accepted Answer

Welcome back. I am so glad you're here. We're asked to simplify the following expression. We're given 225 raised to the negative one half. Our answer choices are answer choice. A 1/15 answer choice, B 25 answer choice C 15, an answer choice D negative five, right? The first thing we notice for simplifying is that our 225 is being raised to a negative exponent and exponents do not want to be negative. How do we get rid of that negative in our exponent? Well, if something being raised to a negative exponent is an a numerator, it needs to move down to a denominator. If something being raised to a negative exponent is in a denominator, it needs to move up to the numerator and that will get rid of the negative in the exponent. This 225 race to the negative one half is in an unwritten numerator with the denominator of one. So it needs to move down to the denominator as it does. So our new numerator becomes one and that's divided by 225. Now raised to the positive one half, we can still do a little bit more simplification. We can simplify this 225 race to the one half we recall from previous lessons that what's in the denominator of a rational exponent. So in this case, two is going to be the root that we're taking of the number being raised to that rational exponent. So this whole thing is equal to one divided by and then we're taking the square root of 225. We know that what's in the numerator of our rational exponent, which in this case is one is the exponent that the whole thing is being raised to that has the rational exponent. So it's the square root of 2225 raised to the first power. But we don't really need to worry about that raised to the first power part. Mostly we focus on the square root of 225. Well, the square root of 225 is 15 and 15 raised to the first power is 15. So this whole thing is equal to 1/15. We look at our answer choices and that matches with answer choice. A 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. 49^-½

Key Concepts

Rational Exponents

Negative Exponents

Simplification of Expressions

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