Factor (a^mb^m)*(4(a^(m+1)b^(m+1)))*2

Math
(ambm)⋅(4(am+1bm+1))⋅2
Remove unnecessary parentheses.
ambm⋅4am+1bm+1⋅2
Combine exponents.
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Multiply am by am+1 by adding the exponents.
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Move am+1.
am+1ambm⋅4bm+1⋅2
Use the power rule aman=am+n to combine exponents.
am+1+mbm⋅4bm+1⋅2
Add m and m.
a2m+1bm⋅4bm+1⋅2
a2m+1bm⋅4bm+1⋅2
Multiply bm by bm+1 by adding the exponents.
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Move bm+1.
a2m+1(bm+1bm)⋅4⋅2
Use the power rule aman=am+n to combine exponents.
a2m+1bm+1+m⋅4⋅2
Add m and m.
a2m+1b2m+1⋅4⋅2
a2m+1b2m+1⋅4⋅2
Multiply 2 by 4.
a2m+1b2m+1⋅8
a2m+1b2m+1⋅8
Factor (a^mb^m)*(4(a^(m+1)b^(m+1)))*2

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