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Stretching the limits of "reasonable way" here, but the expressions are separated.

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Stretching the limits of "reasonable way" here, but the expressions are separated.

Explanation

First expression:

XH'^'i'='XJ
XH % implicitly take input A, save it to clipboard H
'^' % push literal '^'
i % take input B
'=' % push literal '='
XJ % copy '=' to clipboard J, we'll use this twice more so it's worth it

Second expression:

2G:"H'*']xJ
2G % paste the second input (B) again
:" % do the following B times
 H % paste A from clipboard H
 '*' % push literal '*'
] % end loop
x % delete the final element (at the moment we have a trailing *)
J % paste '=' from clipboard J

Third expression:

&Gq^:"H'+']xJ
&G % paste all of the input, ie push A and B
q % decrement B
^ % power, giving A^(B-1)
:" % do the following A^(B-1) times 
 H % paste A from clipboard H
 '+' % push literal '+'
] % end loop
x % delete the final element (at the moment we have a trailing +)
J % paste '=' from clipboard J

Fourth expression:

&G^:"1'+']x
&G % paste all of the input, ie push A and B
^ % power, giving A^B
:" % do the following A^B times 
 1 % push 1
 '+' % push '+'
] % end loop
x % delete the final element (at the moment we have a trailing +)
 % (implicit) convert all to string and display

MATL, 46 bytes

XH'^'i'='XJ2G:"H'*']xJ&Gq^:"H'+'XI]xJ&G^:"1I]x

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Stretching the limits of "reasonable way" here, but the expressions are separated.

MATL, 46 bytes

XH'^'i'='XJ2G:"H'*']xJ&Gq^:"H'+']xJ&G^:"1'+']x

Try it online!

Stretching the limits of "reasonable way" here, but the expressions are separated.

MATL, (削除) 64 (削除ここまで) 58 bytes

VXH94ciV&YcD2G:"H42c]x&YcD&Gq^:"H43cXI]x&YcD&G^:"1VI]x&YcD

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MATL, 46 bytes

XH'^'i'='XJ2G:"H'*']xJ&Gq^:"H'+'XI]xJ&G^:"1I]x

Try it online!

Stretching the limits of "reasonable way" here, but the expressions are separated.