irrational-power-irrational (illustrates re-use of strings) Prove: {@thm@}

[[parsons input="ans1" clone="true" height="550px"]] {# stackjson_stringify(proof_steps) #} [[/parsons ]] ]]>

{@proof_display_para(tal[1], proof_steps)@}

{@proof_display_para(tal[2], proof_steps)@}

Can you see the differences between these proofs?]]> 1.0000000 0.1000000 0 2023111600 [[feedback:prt1]] {@map(first, proof_steps)@} 1 0 0 Correct answer, well done.]]> Your answer is partially correct.]]> Incorrect answer.]]> . dot 1 i cos-1 lang [ ans1 string proof_parsons_key_json(ta, []) 15 1 0 0 1 0 0 0 0 hideanswer ans2 string proof_display(ta, proof_steps) 15 1 0 0 1 0 0 0 0 prt1 1.0000000 1 1 sa:proof_parsons_interpret(ans1); [pd,saa]:proof_assessment(sa, proof_alternatives(ta)); 0 AlgEquiv pd 0 0 = 1 -1 prt1-1-T = 0 -1 prt1-1-F {@proof_assessment_display(saa, proof_steps)@} 77 1 Test case assuming the teacher's input gets full marks. ans1 proof_parsons_key_json(ta, []) ans2 proof_display(ta, proof_steps) prt1 1.0000000 0.0000000 prt1-1-T log-two-three-irrational Prove: {@thm@}

Drag those strings needed to construct a correct proof.

[[parsons input="ans1" height="650px"]] {# stackjson_stringify(proof_steps) #} [[/parsons ]]

(You can drag to re-order or remove strings. Double tap to add at the end, or remove.)

]]> Prove: {@thm@}

{@proof_display(first(tal), proof_steps)@}]]> 1.0000000 0.1000000 0 2023111600 [[feedback:prt1]] {@map(first, proof_steps)@} 1 0 0 Correct answer, well done.]]> Your answer is partially correct.]]> Incorrect answer.]]> . dot 1 i cos-1 lang [ ans1 string proof_parsons_key_json(ta, proof_steps) 15 1 0 0 1 0 0 0 0 hideanswer ans2 string proof_display(ta, proof_steps_prune(proof_steps)) 15 1 0 0 1 0 0 0 0 prt1 1.0000000 1 1 sa:proof_parsons_interpret(ans1); [pd,saa]:proof_assessment(sa, proof_alternatives(ta)); 0 AlgEquiv pd 0 0 = 1 -1 prt1-1-T = 0 -1 prt1-1-F {@proof_assessment_display(saa, proof_steps)@} 1326674135 487104984 737200307 1172493662 897001585 1561808185 1927179470 2007574041 581975935 1734890149 1 Test case assuming the teacher's input gets full marks. ans1 proof_parsons_key_json(ta, []) ans2 proof_display(ta, proof_steps) prt1 1.0000000 0.0000000 prt1-1-T Parsons plot [[input:ans1]] [[validation:ans1]]

]]> 1.0000000 0.1000000 0 2023111600 [[feedback:prt1]] {@map(first, proof_steps)@} 1 0 0 Correct answer, well done.]]> Your answer is partially correct.]]> Incorrect answer.]]> . dot 1 i cos-1 lang [ ans1 string proof_parsons_key_json(ta, []) 15 1 0 0 1 0 0 0 0 hideanswer prt1 1.0000000 1 1 sa:proof_parsons_interpret(ans1); [pd,saa]:proof_assessment(sa, proof_alternatives(ta)); 0 AlgEquiv pd 0 0 = 1 -1 prt1-1-T = 0 -1 prt1-1-F {@proof_assessment_display(saa, proof_steps)@} 1733122457 1657629229 2099022223 1441581320 1603372470 1 Test case assuming the teacher's input gets full marks. ans1 proof_parsons_key_json(ta, []) prt1 1.0000000 0.0000000 prt1-1-T