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- Simplify ( 6a^-2bc^-3/4ab^-3c^2 ) ÷ ( 5a^-3 b^2^-1/3ab^-2c^3 )
Question 1:
Simplify ( 6a^-2bc^-3/4ab^-3c^2 ) ÷ ( 5a^-3 b^2^-1/3ab^-2c^3 ) A. 9/10ac
B. 9/10ac^-1
Feedback Apply the algebra law a ÷ b = a x 1/b
= ( 6a^-2bc^-3/4ab^-3c^2 ) x ( 3ab^-2c^3/5a^-3 b^2c^-1 )
= ( 6a^-2 bc^-3 x 3ab^-2c^3) / ( 4ab^-3c^2 x 5a^-3b^2c^-1 )
Apply the law of Fractional Exponents and Laws of Exponents
(a^m)(a^n) = a^m+n
a^m/a^n=a^m-n
= 18a^-2 + 1 b^1 - 2 c^-3 + 3 / 20a^1 - 3 b^-3 + 2 c^2 - 1
= 9a^-1b^-1c^0/ 10a^ - 2 b^-1c^1
= ( 9/10 ) a^-1 + 2 b^-1 + 1 c^0 - 1
= ( 9/10 ) a^1.b^0.c^-1
= ( 9/10 ) ac^-1 [∵ b0 = 1]
= ( 6a^-2bc^-3/4ab^-3c^2 ) x ( 3ab^-2c^3/5a^-3 b^2c^-1 )
= ( 6a^-2 bc^-3 x 3ab^-2c^3) / ( 4ab^-3c^2 x 5a^-3b^2c^-1 )
Apply the law of Fractional Exponents and Laws of Exponents
(a^m)(a^n) = a^m+n
a^m/a^n=a^m-n
= 18a^-2 + 1 b^1 - 2 c^-3 + 3 / 20a^1 - 3 b^-3 + 2 c^2 - 1
= 9a^-1b^-1c^0/ 10a^ - 2 b^-1c^1
= ( 9/10 ) a^-1 + 2 b^-1 + 1 c^0 - 1
= ( 9/10 ) a^1.b^0.c^-1
= ( 9/10 ) ac^-1 [∵ b0 = 1]
C. 9/10ac^2
D. None of the above
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