Method I Using the law of indices Change the 42 to base 2 so that the base 2 s can simplify each other. 4=2×2 42=(2×2)2 But (am×bn)c=am×c××bn×c 2=21 (2×2)2=(21×21)2 (2×2)2=21×2×21×2 (2×2)2=22×22
Law of multiplication of indices am×an=am+m (2×2)2=22+2 (2×2)2=24 Alternate Solution (am)n=am×n 4=2×2=22 42=(22)2=22×2=24
22×32
42×33
=
22×32
24×33
Law of division of indices
am
an
=am−n
22×32
24×33
=22−4×32−3=2−2×3−1 But a−b=
1
ab
2−2×3−1=
1
22
×
1
31
22=2×2=4 31=3
2−2×3−1=
1
4
×
1
3
=
1×1
4×3
=
1
12
Method II Change the indices to multiplication, cancel out and simplify 22=2×2 42=4×4 32=3×3