How do you simplify this expression: #(a^8a^6)^(1/7)/a^2#?

Question

2828 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-12-14T14:17:45

1

Step 1) Combine the terms within the parenthesis using the rule for exponents:

#color(red)(x^ax^b = x^(a + b))#

#((a^(8+6))^(1/7))/a^2#

#((a^14)^(1/7))/a^2#

Step 2) Simplify the numerator by using the rule for exponents:

#color(red)((x^a)^b = x^(a*b))#

#(a^(14 * 1/7))/a^2#

#a^2/a^2#

Step 3)

We can use the rule from math: #color(red)(x/x = 1)#

#a^2/a^2 = 1#

Or, we can use the rule for exponents:

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

#a^2/a^2 = a^(2-2) = a^0 = 1#

Answer 2 · 2016-12-14T14:27:45

The answer is 1.

Here are some rules when working with exponents:

#1.# #" "x^m xx x^n = x^(m+n)#
#2.# #" "x^m div x^n = x^(m-n)#
#3.# #" "(x^m)^n = x^(mn)#
#4.# #" "x^0 = 1#

Now, to solve this question, it can be written as:

#" "(a^8xxa^6)^(1/7) div a^2#
#=> (a^(8+6))^(1/7) div a^2#
#=> a^(14xx1/7) div a^2#
#=>a^2 div a^2 = a^(2-2) = a^0 = 1#