need help with indices simplify

• Aug 11th 2009, 11:53 PM
realistic
need help with indices simplify
simplify
(9 x 3^2)^3 / (3 x 27 ) ^2

similar

(16 x 4)^2 / (2 x 8)^3

got stuck on these if some could help out and explain working would be great
I tried changing them to the same base so i could apply rules but stull having probs (Bow)
• Aug 12th 2009, 12:00 AM
red_dog
The numerator:

$9=3^2$

$9\cdot 3^2=3^2\cdot3^2=3^4$

$(9\cdot 3^2)^3=(3^4)^3=3^{12}$

The denominator:

$27=3^3$

$3\cdot 27=3\cdot 3^3=3^4$

$(3\cdot 27)^2=(3^4)^2=3^8$

Now, $\frac{(9\cdot 3^2)^3}{(3\cdot 27)^2}=\frac{3^{12}}{3^8}=3^{12-8}=3^4=81$

Can you do the other in a similar way?
• Aug 12th 2009, 12:06 AM
realistic
yes i see now thanks alot (Bow)