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

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Answer 1 · 2017-09-18T12:33:35

#6#

#"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 · 2017-09-18T12:33:44

See a solution process below:

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#