Simplify.
-$\frac { \sqrt [ 3 ] { 640 } } { \sqrt [ 3 ] { 10 } }$
A) 5
B) 3
C) 4
D) 6

Question

Quizplus · Accepted Answer

We can simplify the numerator and denominator by finding the prime factorization of 640 and 10. 
640 = 2^7 * 5 and 10 = 2 * 5. 
Taking the cube root of these, we get: 
$\sqrt [ 3 ] {640} = \sqrt [ 3 ] {2^7 * 5} = 2\sqrt [ 3 ] {80}$ 
$\sqrt [ 3 ] {10} = \sqrt [ 3 ] {2 * 5} = \sqrt [ 3 ] {2} \sqrt [ 3 ] {5}$ 
Substituting these into the original expression, we get:
$\frac { \sqrt [ 3 ] { 640 } } { \sqrt [ 3 ] { 10 } } = \frac {2\sqrt [ 3 ] {80}}{\sqrt [ 3 ] {2} \sqrt [ 3 ] {5}}$ 
Simplifying this, we can cancel out the common factors: 
$\frac {2\sqrt [ 3 ] {80}}{\sqrt [ 3 ] {2} \sqrt [ 3 ] {5}} = 2\sqrt [ 3 ] {16} = 2*4 = 8$ 
Therefore, the answer is C: 4.

Simplify - 6403103\frac { \sqrt [ 3 ] { 640 } } { \sqrt [ 3 ] { 10 } }310​3640​​

Simplify
- $\frac { \sqrt [ 3 ] { 640 } } { \sqrt [ 3 ] { 10 } }$