Question

Applying the different laws of exponents, how to simplify `6^(5/3)/(6^(2/3))` ?

Answer 1

`6`

Explanation:

`"using the "color(blue)"law of exponents"`

`•color(white)(x)a^m/a^n=a^((m-n))`

`rArr6^(5/3)/6^(2/3)=6^((5/3-2/3))=6^(3/3)=6^1=6`

Answer 2

See a solution process below:

Explanation:

First, use this rule of exponents to eliminate the fraction:

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

`6^color(red)(5/3)/6^color(blue)(2/3) = 6^(color(red)(5/3)-color(blue)(2/3)) =6^(3/3) = 6^1`

Now, use this rule of exponents to complete the simplification:

`a^color(red)(1) = a`

`6^color(red)(1) = 6`