How do you simplify #\frac { a ^ { \frac { 1} { 5} } a ^ { \frac { 6} { 5} } } { a ^ { \frac { 9} { 3} } }#?
1 Answer
Explanation:
Since the base of the exponents are all
With that, we will get
We can add the fractions of the exponent in the numerator to get:
Similar to the exponent product rule, we can use the divisibility rule which states that
Using that, we will simplify the equation to
We can also now reduce the fraction
New expression:
Just like subtracting regular fractions, we need to change the denominator of both fractions to a common multiple, in this case, it is
Subtracting the exponents gets us
Now, using the negative exponent rule, we know that
This will get us
We now have to use the fractional exponent law:
Finally, since