In Exercises 77–90, simplify each expression. Include absolute va...

Question

In Exercises 77–90, simplify each expression. Include absolute value bars where necessary.__³√x³

Accepted Answer

Hey, everyone in this problem, we're asked to rewrite the following algebraic expression in the simplest form possible. And to use absolute value bars if needed the expression you given is the 7th root of K to the exponent seven, we have four answer choices. Option A is seven K. Option B is the absolute value of seven K. Option C is K and option D is the absolute value of K. Let's start by rewriting what we were given. So we have the seventh root of K to the exponent seventh. Now recall if we have the en route of A, we can write this as a to the exponent one divided by N. In our problem, we're taking the seventh route. So N S seven, so we can write this as K to the exponent seven to the exponent one divided by seven. Now we have an exponent raised to an exponent. Recall the power rule. If we have A to the exponent M to the exponent N, we can simplify this by multiplying those exponents and writing this as a to the exponent M multiplied by N. In our case, we have an exponent seven to an exponent one divided by seven, seven, multiplied by one divided by seven is equal to one. So we can simplify this just as K to the exponent one, which is equal to K. And this is our simplest algebraic expression or the simplest form of the algebraic expression that we can find the correct answer is K which corresponds with answer choice. C thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 77–90, simplify each expression. Include absolute value bars where necessary.__³√x³

Key Concepts

Cube Root

Absolute Value

Simplifying Expressions

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