Question #024f4

1 Answer
Apr 16, 2017

Answer:

See the entire solution process below:

Explanation:

In the standard order of operations you first, execute the terms with exponents:

#3 * color(red)(3^5)/color(blue)(3^2) = 3* 243/9 = 3 * 27 = 81#

Another way to evaluate this is using various rules of exponents:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#3 * 3^color(red)(5)/3^color(blue)(2) = 3 * 3^(color(red)(5)-color(blue)(2)) = 3 * 3^3#

Then:

#a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#3 * 3^3 = 3^color(red)(1) * 3^color(blue)(3) = 3^(color(red)(1) + color(blue)(3)) = 3^4 = 81#