PLSSS C= (12^(3) . 6^(5) )/(9^(4) . 2^(10))

Question

PLSSS

C=
`(12^(3) . 6^(5) )/(9^(4) . 2^(10))`

Answer 1

2

Explanation:

The trick here is to reduce each of the bases to lowest form first

`12 = 3.4 = 3 .2.2 = 3.2^(2)\\12^(3) = (3.2^(2) )^(3) = 3^(3)2^(6) \\6 = 3.2\\6^(5) = (3.2)^(5) = 3^(5) .2^(5) \\\\Numerator = 3^32^63^52^5 = 3^82^(11)\\Denominator computation\\9 = 3^2\\9^(4) = (3^(2) )^4 = 3^(8) \\Denominator = 3^82^(10) \\\\(Numerator)/(Denominator ) =\frac{{3^8}{2^(11) }}{3^82^(10)} = \frac{2^(11)} {2^(10)} = 2^1 = 2`