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Simplify and express each of the following in exponential form: (2^8 × a^5 )/ (4^3 × a^3 )

 Simplify and express each of the following in exponential form:
 (2^8 × a^5 )/ (4^3 × a^3 )

Grade:12

2 Answers

Harshit Singh
askIITians Faculty 5964 Points
7 months ago
Dear Student

(4)^3can be written as = (2 × 2)^3
= (2^2)^3

(5^2)^4 can be written as = 2^2×3 = 2^6 ... [∵(a^m)^n ) = a^mn
Then
= (2^8× a^5)/ (2^6× a^3)
=2^8-6 × a^5-3 ... [∵a^m÷a^n = a^m-n ]
= 2^2× a^2
= 2a^2 ... [∵(a^m)^n ) = a^mn

Thanks
Shraddha Singh
273 Points
2 months ago
Dear Student,
 
4³ can be written as (2×2)³.
 
(28 × a) / (2×2)³ × a³
= 28-6 × a5-3 
= 2² × a²
= (2a)² or 4a²
 
Hope it helps!
Thank you ✌️

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