Answer:
Step-by-step explanation:
This can be simplified into
[tex]8^{\frac{1}{3}}*320^{\frac{1}{3}}[/tex]
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
[tex]\sqrt[3]{320}= \sqrt[3]{5*2^6}[/tex]
Split that 2^6 up into increments of 3's to make the simplifying a bit easier:
[tex]\sqrt[3]{5*2^3*2^3}[/tex]
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:
[tex]4\sqrt[3]{5}[/tex]
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:
[tex]8\sqrt[3]{5}[/tex]
