Question

Which of the following is equal to the expression below?

Answer 1

Answer:

Step-by-step explanation:

This can be simplified into

$8^{\frac{1}{3}}*320^{\frac{1}{3}}$

which is saying that you are taking the cubed root of each of those bases.  The cubed root of 8 comes out evenly, to 2 (since 2*2*2 = 8).  The cubed root of 320 is not so simple.  To find it, find the complete factorization of 320.  320 factors to: 5 * 2*2*2*2*2*2 or

$\sqrt[3]{320}= \sqrt[3]{5*2^6}$

Split that 2^6 up into increments of 3's to make the simplifying a bit easier:

$\sqrt[3]{5*2^3*2^3}$

Because the index (the little number sitting in the bend of the radial sign) matches the power on both the 2's we can pull both the 2's out front, leaving:

$4\sqrt[3]{5}$

but don't forget that we already found that the cubed root of 8 was 2, so multiply that 2 by the 4 to get:

$8\sqrt[3]{5}$

Answer 2

Answer:

C)

Step-by-step explanation: