Question

Cube root of -686/-2662 by prime factorisation method.

Answer 1

Answer:

$\frac{7}{11}$ or 0.6363

Step-by-step explanation:

-686/-2662 = 686/2662

686 = 2 x 7 x 7 x 7

2662 = 2 x 11 x 11 x 11

=  (2 x 7 x 7 x 7) / (2 x 11 x 11 x 11)

=  7 x 7 x 7/ 11 x 11 x11

= $7^{3}$ ÷ $11^{3}$

According to exponential law #5,

a^{n} ÷ b^{n} = (a÷b)^{n}

= (7/11)³

since we have to find cube root,

∛(7/11)³

= (7/11) or 0.6363636363(recurring)

the answer is   $\frac{7}{11}$ / 0.6363

Hope it helps,

Byeeee