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The derivation process of a mathematical formula. I don't understand this part. Please translate it (in detail)
Algorithm of exponential function:

(a^x)*(a^x)=a^(x+x)?

(a^x)/(a^x)=a^(x-x)?

a=(a^x)^ 1/x

In the same way; In a similar way

? a^x=M^y

? a^x=m^(y-(y- 1))*m^(y- 1)

Substitute m y = a x into the corresponding item on the left,

m^y=m^(y-(y- 1))*m^(y- 1)

? M^y/M^(y- 1)=M^ 1

? M (y-(y- 1)) = m (then use the third exponential algorithm).

[(m^y)^ 1/y]^(y-(y- 1))=m

Substitute m y = a x into the corresponding item on the left,

[(a^x)^ 1/y]^(y-(y- 1))=m

? (a^x)^( 1/y)=M

? a^(x/y)=M

Prove completion.