Question

4) Simplify :
(i) (125 ×x^(-3))/(5^(-3)×25 ×x^(-6) )
(ii) (16×10^2×64)/(2^4×4^2 )

Answer 1

it's better to use * for multiplication, so it does not get confused with x, a variable. So,
(125*x^(-3))/(5^(-3)*25*x^(-6) )
= (5^3 x^-3)/(5^-3 * 5^2 x^-6)
= (5^3 x^-3)/(5*-1 x^-6)
= 5^(3-(-1)) x^(-3-(-6))
= 5^4 x^3
= 625 x^3

Answer 2

(i) (125 ×x^(-3))/(5^(-3)×25 ×x^(-6) )
= [5*5*5/x*x*x ] / [ (5*5)/ {5*5*5} / (x*x*x*x*x*x) ]
= [5*5*5/x*x*x ] * [ {5*5*5} / (x*x*x*x*x*x) ] / (5*5)
= 5*5*5*5 * (x*x*x)
= 625 x^3
your turn now

Answer 3

hint
16 = 4^2
64 = 16* 4 = 4^3
2^4 =( 2^2)^2 = 4^2

Answer 4

(125 ×x^(-3))/(5^(-3)×25 ×x^(-6) )

write it this way, easier to read:
(125x^-3)/(5^-3*25*x^-6 ) , the * is often used as multiplication, if an exponent is a monomial you don't need brackets around it.
= (125/x^3)/((1/125)(25))*x^6
= 125*5*x^3
= 625x^3

or, even simpler ...
(125x^-3)/(5^-3*25*x^-6 )
= 125/(25/125) x^(-3+6)
= 625x^3 or (5^4)(x3)

looking at the 2nd one, I see all powers of 2 and a 10^2
(16×10^2×64)/(2^4×4^2 )
= (2^4)(100)(2^6)/( (2^4)(*2^4))
= 100(2^10)/2^8
= 100(2^2) = ...