Simplify each radical. Assume all variables represent positive re...

Question

Simplify each radical. Assume all variables represent positive real numbers. ∛(25 (-3)⁴ (5)³ )

Accepted Answer

Hey everyone here we are asked to simplify the following expression where we have the third root of 16 times the quantity of negative two raised to the six power times the quantity of six cubed. So now the key here in simplifying this expression is to find as many cubed terms as possible from this expression That's underneath the root. So we can start with the first value from that expression here which is 16. Well 16 breaks up into two times two which is four times two gives us eight and times another two gives us 16. So we see that 16 is equivalent to two times two to the third power. And now we can move on to the next term where we have the quantity of negative two raised to the sixth power. Well we can break up this sixth power into the quantity of negative two raised to the third power times the quantity of negative two raised to the third power. And lastly our last term here is six cubed while it is already a cubed term. So we do not need to modify it in any way or expand it. So with this we just now need to rewrite our original expression with our expanded values. So we have the third root of two times too cute Times the quantity of -2, cute times the quantity of another negative too cute. And Lastly Times six, Cute. And with this, all that is left to do is take the cubed root of each of these terms here to simplify our expression and so outside of the root we see that we are left with two times, negative two times, negative two Times six. And inside the route we are just left with this too. So this these values are all multiplied by the third root of just two since this expression cannot be simplified any further. And so now we just need to finish up simplifying by multiplying these terms out Outside of the route together. So doing this, we are left with 48 times the third root of two. And this is our final simplified form of our original expression, which leaves us with answer choice. A thanks for watching. I hope you found this video helpful and I'll see you again next time.

Simplify each radical. Assume all variables represent positive real numbers. ∛(25 (-3)⁴ (5)³ )

Key Concepts

Radical Expressions

Properties of Exponents

Simplifying Radicals

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