Q. 81

Express each of the following in single exponential form:

(a) 23 × 33

(b) 24 × 42

(c) 52 × 72

(d) (– 5)5 × (–5)

(e) (– 3)3 × (– 10)3

(f) (– 11)2 × (– 2)2

Answer :

(a) According to law of indices:


am × bm = (ab)m


Here in the question,


23 × 33 = (3 × 2)3


= 63


(b) 23 = 2 × 2 × 2 × 2


= 16


42 = 16


24 × 42 = 16 × 16


= 162


(c) According to law of indices:


am × bm = (ab)m


Here in the question,


52 = 25


72 = 49


52 × 72 = (5 × 7)2


= 352


(d) (– 5)5 × (–5) = (– 5)5 + 1


= (– 5)6


(e) According to law of indices:


am × bm = (ab)m


Here in the question,


(– 3)3 × (– 10)3 = (-3 × -10)3


= (30)3


(f) According to law of indices:


am × bm = (ab)m


Here in the question,


(– 11)2 × (– 2)2 = (-11 × -2)2


= 222


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