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.

x^⅘
x^⅕

Accepted Answer

Hey, everyone in this problem, we're asked to simplify the following expression by using the properties of rational exponents. We're told to assume that B is greater than zero. The expression we're given is B to the exponent 6 7th divided by B to the Exponent 2/7. We're given four answer choices. Option A B to the exponent 4/7. Option B B to the exponent 12 divided by 49. Option C B to the exponent eight divided by seven and option DB cubed, we're gonna start by rewriting the expression we were given. So we have B to the exponent 6 7th divided by B to the exponent 2 7th. Now we want to combine this into a single term. We're dividing two things with the same base. How can we simplify that? I recall if we have X to the exponent M divided by X to the exponent N, we can write this as X to the exponent M minus N. This is one of our properties of rational exponents. So we divide two things with the same base. We can simplify it into a single term. We have that same base and then we subtract the exponent from the numerator minus the exponent from the denominator. We apply that to our problem. We have B to the exponent 6/ minus two sevens. OK? We keep our base which is B, we take the exponent from the numerator 6/7 and subtract the exponent from the denominator 2/7. Now we have a single term and we're just left with simplifying the exponent. So we have six divided by 7 -2, divided by seven. So we get B to the exponent four divided by seven. And that is our simplified expression. That's what the problem was asking us to find. We found that the correct answer is B to the exponent four divided by seven which corresponds with answer choice A. That's it for this one. Thanks everyone for watching. I hope this video helped.

In Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. x^⅘ x^⅕

Key Concepts

Rational Exponents

Properties of Exponents

Simplifying Expressions

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