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√(−5)³

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 given is the cube root of negative six to the exponent three, we have four answer choices. Option A is the square root of six. Option B is -6. Option C is six. In option D, this expression cannot be simplified further. We're gonna start by writing the expression we were given. So we have the cube root of negative six to the exponent three. Now recall if we have the N root of A, we can write this as a to the exponent one divided by N OK. So we can write roots or radicals in terms of exponents and vice versa. If we apply this to our problem, we can write this cube root as an exponent of one divided by three. So expression beca becomes negative six cubed to the exponent 1/3. Now we have an exponent raised to an exponent. So we call our power rule if we have a to the exponent M raised to the exponent, and we can simplify the exponents by multiplying them together. So we get A to the exponent M multiplied by N. In our case, we have negative six to the exponent three to the exponent one divided by three, we multiply the exponents together to simplify three, multiplied by one third, gives us just one. So we have negative six to the exponent one which is just equal to negative six. And so simplifying the algebraic expression we were given, we found the correct answer is negative six which corresponds with answer choice B 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√(−5)³

Key Concepts

Cube Root

Exponentiation

Absolute Value

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