25·a^(-5)·b^(-8) : 5·a^4·b
= [ 25·a^(-5)·b^(-8) ] / [ 5·a^4·b ] (ratios indicate division)
= [ 25 / ( a^5 · b^8 ) ] / [ 5·a^4·b ] (negative exponents become positive when placed in the denominator)
= [ 25 / ( a^5 · b^8 ) ] · [ 1 / ( 5·a^4·b ) ] (division is replaced by multiplication of the reciprocal)
= [ 25 · 1 ] / [ a^5 · b^8 · 5·a^4·b ] (multiplying numerators times nums and denominators time denoms)
= 25 / [ 5 · a^9 · b^9 ] (simplifying)
= 5 / [ a^9 · b^9 ] (cancelling like factors)
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