simplify by using the laws of indices
(4 m²n²)³ by (2mn³)²
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Step-by-step explanation:
64m^6n^6 by 4m^2n^6
16m^4
Answered by
1
(4*m^2*n^2)^3 / (2*m*n^3)^2
= (4^3/2^2) * ((m^2*n^2)^3 / (m*n^3)^2)
= (64/4) * ((m^2*n^2)^3 / (m*n^3)^2)
= (16) * ((m^2*n^2)^3 / (m*n^3)^2)
= (16) * ((m^2)^3/(m)^2) * ((n^2)^3/(n^3)^2)
[ Using (a^m)^n = (a)^m*n ]
= (16) * ((m)^6/(m)^2) * ((n)^6/(n^6))
[ Using (a)^m/(a)^n = (a)^(m - n) ]
= (16) * (m)^(6 - 2) * (n)^(6 - 6)
= (16) * (m)^4 * (n)^0 [ Using (n)^0 = 1 ]
= (16) * (m)^4 ——> Answer
= (4^3/2^2) * ((m^2*n^2)^3 / (m*n^3)^2)
= (64/4) * ((m^2*n^2)^3 / (m*n^3)^2)
= (16) * ((m^2*n^2)^3 / (m*n^3)^2)
= (16) * ((m^2)^3/(m)^2) * ((n^2)^3/(n^3)^2)
[ Using (a^m)^n = (a)^m*n ]
= (16) * ((m)^6/(m)^2) * ((n)^6/(n^6))
[ Using (a)^m/(a)^n = (a)^(m - n) ]
= (16) * (m)^(6 - 2) * (n)^(6 - 6)
= (16) * (m)^4 * (n)^0 [ Using (n)^0 = 1 ]
= (16) * (m)^4 ——> Answer
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