Question

Find m if : (-2/5) power -13 * (5/-2) power 8 = (-2/5) power -2m+1

Answer 1

Hi ,

( -2/5 )^-13 * ( 5 /-2 )^8 = ( -2/5 ) ^ -2m + 1
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we know that ,

1 ) ( a/b )^-m = ( b/a )^m

2 ) a^m * a^n = a^m +n

3 ) if a^m = a^n then m = n

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( -5/2 )^13 * ( -5/2 )^8 = ( -5/2 )^-(-2m + 1 )

( -5/2 )^ 13 + 8 = ( -5/2 ) ^ 2m - 1

( -5/2 )21 = ( -5/2 )^2m - 1

Therefore ,

21 = 2m - 1

21 + 1 = 2m

22 = 2m

22/ 2 = m

11 = m

m = 11

I hope this helps you.

:)