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a) 3 × 3^4 × 2^5/2 × 4^2
Ans. 3 × 3^4 × 2^5/2 × (2^2)^2
= 3^1+4 × 2^5/2 × 2^4
=3^5 × 2^5/2^1+4
=3^5 × 2^5/2^5
=3^5 × 2^5 - 5
=3^5 × 2^0
=3^5 × 1
=3^5
or
=3 × 3 × 3 × 3 × 3
=243
b) [(4^3)^2 × 4^4] ÷ 4^14
Ans. [4^6 × 4^4] ÷ 4^14
= [4^6 + 4] ÷ 4^14
= 4^10 ÷ 4^14
= 4^10 - 14
= 4^-4
= 1/4^4
or
= 1/4 × 4 × 4 × 4
= 1/256
c) 8^3 × a^5 × b^2/2^6 × a^3 × b
Ans. (2^3)^3 × a^5 - 3 × b^2 - 1/2^6
= 2^9 × a^2 × b/2^6
= 2^9 - 6 × a^2 × b
= 2^3 × a^2 × b
= 2 × 2 × 2 × a^2 b
= 8a^2 b
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