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

2 Answers
Dec 14, 2016

1

Explanation:

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

Dec 14, 2016

The answer is 1.

Explanation:

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