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Surds and Indices



  2. Question:8134 
    Answer
    (34)34 = 34×34 =33 = 27






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  3. Question:(164)-56 
    Answer
    (164)-56

=6456

=(26)56

=26×56

=25

=32






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  4. Question:256-14 
    Answer
    256-14

=(1256)14

=[(14)4]14

=(14)4×14

=14






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  5. Question:(xbxc)(b2+c2+bc) x (xcxa)(c2+a2+ca) x (xaxb)(a2+b2+ab) 
    Answer
    =(xb-c)(b2+c2+bc) x (xc-a)(c2+a2+ca) x (xa-b)(a2+b2+ab)

=x(b-c)(b2+c2+bc)    x  x(c-a)(c2+a2+ca)    x  x(a-b)(a2+b2+ab)

= x(b3-c3)  x x(c3-a3)  x x(a3-b3)

=x(b3-c3)+(c3-a3)+(a3-b3)

=x0

=1






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  6. Question:(212×313×41410-15×535/343×5-754-35×6) 
    Answer
    212×313×41410-15×535×4-35×6343×5-75

= 212×313×2122-15×5-15×535×(22)-35×(2×3)343×5-75

= 212×313×2122-15×5-15×535×2-65×2×3343×5-75

= 212+12+15-65+1.313+1-435-15+35-75

= (21×30×51)

= (2 x 1 x 5)
= 10






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