In Exercises 1–20, use radical notation to rewrite each expressio...

Question

In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible.

-16^¼

Accepted Answer

Hey, everyone in this problem, we're asked to write the given expression in a radical notation. And to write the answer in simplified form, the expression we given is -81 to the exponent 1/4. We have four answer choices. Option A negative the fourth route of or three. Option B negative square root of 81 to the exponent four or negative three. Option C negative the fourth route of or negative three. And option D the fourth through of 81 or negative three, we're gonna start by rewriting what we were given. So we have negative 81 to the exponent 1 4th. Now I wanna make it clear. OK? That negative is outside. It's not being applied to this exponent. OK? This exponent does not apply to the negative, but just to be clear, we're gonna write it in brackets. OK? So we have 81 to the exponent 1/4 in brackets and then negative is outside. Now, we want to write this in radical notation right now we have an exponent. OK? So recall how can we relate exponents to radicals if we have a to the exponent one divided by then we can write this as the nth route of A. This allows us to relate the two. Now, in our case, the A value is 81 and that's the base of our exponent. The exponent is one divided by four. So we have an end value of four. This means that we have negative the four through of 81. So we found the radical notation to be negative the fourth route of 81. So we know we're looking at option either A or C. Now let's simplify this in order to figure out which answer choice we have. Now we have negative the fourth route of 81. So we're looking for a number whose ex raise to the exponent four is equal to 21 or 81 sorry, not 21 81. OK? So some number to the exponent four equals 81 that number is three. And so we get that this is equal to negative 3. OK? 3 to the exponent four is equal to 81. So the fourth root of 81 is equal to three and we get the simplified version is -3. And we found the simplified version, we found the radical notation expression. The correct answer is negative. The 4th route of 81 or -3 which corresponds with answer choice. C thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. -16^¼

Key Concepts

Radical Notation

Exponents and Fractional Powers

Simplifying Radical Expressions

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