How do you evaluate #96^2*(1/3^2)^3*6^2#?

Question

Roman Alvarez · Accepted Answer

The answer can be left in index form. This has more meaning than the actual numbers. #2^12/3^2#

Working with all the bases simultaneously and changing any base to a prime factor would be a faster approach.

#=(2^5*3)^2 * (1/3^2)^3 * (2*3)^2#

Take out the brackets to make it simpler.

#=2^10 * 3^2 * 1/3^6 * 2^2*3^2#

Add the indices to combine like bases:

#=2^12 * 3^4/3^6#

Lastly, deduct the like bases' indices.

#=2^12 /3^2#

Julian Avila · Answer

#4096/9#

Given,

#96^2*(1/3^2)^3*6^2#

Break down the first base into prime numbers.

#=(2^5*3)^2 * (1/3^2)^3 * 6^2#

Simplify.

#=2^10 * 3^2 * 1/3^6 * 6^2#

#=2^10 * 3^2/3^6 * 6^2#

#=2^10 * 3^2/(3^2 * 3^4) * 6^2#

#=2^10 * color(red)cancelcolor(black)(3^2)/(color(red)cancelcolor(black)(3^2) * 3^4) * 6^2#

Break down the last base into prime numbers.

#=2^10 * 1/3^4 * 6^2#

#=2^10 * 1/3^4 * (2*3)^2#

#=2^10 * 1/(3^2*3^2) * 2^2 * 3^2#

#=2^10 * 1/(3^2*color(red)cancelcolor(black)(3^2)) * 2^2 * color(red)cancelcolor(black)(3^2)#

#=2^10 * 1/3^2 * 2^2#

#=1024 * 1/9 *4#

#=4096/9#

Emery Allen · Answer

undefined To evaluate the expression $ 96^2 \times \left(\frac{1}{3^2}\right)^3 \times 6^2 $, follow these steps:

1. Calculate $ 96^2 = 9216 $.
2. Simplify $ \left(\frac{1}{3^2}\right)^3 $ to $ \left(\frac{1}{9}\right)^3 = \frac{1}{729} $.
3. Calculate $ 6^2 = 36 $.
4. Multiply the results together: $ 9216 \times \frac{1}{729} \times 36 = 12 $.