What is $((8m^5n^7)/(2mn^5))^3$ ?

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Answer 1 · 2018-03-26T09:41:38

$64m^12n^6$

Just Use Laws of Indices and you're done.

We have,

$color(white)(xx)((cancel8^4 xxm^5n^7)/(cancel2xxmn^5))^3$

$= ((4m^5n^7)/(mn^5))^3$

$= (4m^5n^7)^3/(mn^5)^3$ [As $(a/b)^m = a^m/b^m$ ]

$= (64m^15n^21)/(m^3n^15)$ [As $(a^m)^n = a^(mn)$ ]

$= 64m^15n^21 xx m^-3n^-15$ [As $a^-m = 1/a^m$ ]

$= 64 xx m^(15 +(-3)) n^(21 +(-15))$ [As $a^(m+n) = a^m xx a^n$ ]

$= 64 xx m^12 n^6 = 64m^12n^6$

Hence Explained.

Answer 2 · 2018-03-26T09:55:03

$color(blue)(=> (64 m^12 n^6)$

$"Given : " ((8m^5n^7)/(2 m n^5))^3$

![ quantbasics.blogspot.in )

$=> ((2^3 m^5 n^7)/(2 m n^5))$

$=> (2^(3-1) * m^(5-1) * n^(7-5))^3,$ $"color(red)(as ( a^m / a^n = a^(m-n))$

$=> (2^2 * m^4 * n^2)^3$

$color(blue)(=> (2^6 m^12 n^6)$ , $color(red)("as "( (a^m)^n = a^(mn))$

$color(blue)(=> 64m^(12)n^6$ , $" as (" 2^6 = 64)$

What is ((8m^5n^7)/(2mn^5))^3((8m^5n^7)/(2mn^5))^3?