baseexpand() cmd

[compsystems]

Hello

Based on order powexpand(a^(m-n)) returns a^m/a^n
In step-by-step algebraic manipulation I believe that a command is needed to expand an exponent, in a base that can be a product, division or expression. I don't know if baseexpand is a good name

0: powexpand(a^(m-n)) returns a^m/a^n

1: baseexpand((x * y)^m ) returns x^m * y^m

2: baseexpand((x / y)^m) returns x^m / y^m

3: baseexpand( (x ^ m)^2) returns x^(2*m)

4: powexpand( 1/a^(n-m) ) returns a^m/a^n


The reverse process can be

0: collect(a^m/a^n) returns a^(m-n)

1: collect(x^m * y^m) returns (x*y)^m )

2: collect(x^m / y^m) returns (x/y)^m )

3: collect( x^m * x^m) returns (x)^2*m

Is this important in the teaching and application of mathematics?