AlgMap-6.7 Write the follwing expression, \(\left( {@a@}\cdot {@v@} \right)^{@b@}\), without brackets.

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]]> Remember that \[\left( {a}\cdot{b} \right)^n = {a^n}\cdot{b^n}. \] Therefore in this example: \[\left({@a@}\cdot {@v@} \right)^{@b@} = \left({@a@}^{@b@} \right)\cdot \left({@v@}^{@b@} \right) = {@a^b@}\cdot{@v^b@}. \]

]]> 1 0.1 0 v:rand([x,y,z,t]); a:rand(7)+2; b:rand([2,3]); ta:expand((a*v)^b); [[feedback:prt1]]

]]> \[\left( {@a@}\cdot {@v@} \right)^{@b@} = {@ta@}.\] 1 0 0 *10 dot 1 i cos-1 lang [ 0 {"author":[{"firstName":"Tony","lastName":"Barnard","institution":"","year":"1999"}],"language":["en"],"isPartOf":"STACK Library - Algebra Refresher","license":"cc-sa-4.0","additional":{"UoE":{"Notes":"This is automatically generated metadata."}},"freeform":{}} ans algebraic ta 15 1 0 0 simp 1 1 1 1 1 prt1 1.0000000 0 1 0 EqualComAss ans ta 0 = 1.0000000 -1 1-0-T = 0.0000000 1 1-0-F 1 AlgEquiv ans a*v^b 0 = 0.0000000 -1 1-1-T Don't forget when you are removing brackets from these types of expression to raise the constant to the power as well as the variable!

]]> = 0.0000000 -1 1-1-F 1214045767 536649773 971070137 374508702 1474212473 1650783818 937873518 455884581 1336036765 1695224112 1 ans ta prt1 1.0000000 0.0000000 1-0-T 2 ans a*v^b prt1 0.0000000 0.1000000 1-1-T