Answer
$8/a^6$
Work Step by Step
$(5a^8/10a^6)^{-3}$ (given)
$(5a^8/5/10a^6/5)^{-3}$ (divide the fraction by 5)
$(a^8/2a^6)^{-3}$ (simplifying the fraction)
$(a^8/a^6/2a^6/a^6)^{-3}$ (divide the fraction by $a^6$)
$(a^2/2)^{-3}$ (simplifying the fraction)
$(a^2)^{-3}/2^{-3}$ (distributing the exponent)
$a^{-6}/1/8$ (simplifying the exponents)
$(1/a^6)/1/8$ (simplifying the exponent)
$(1/a^6)*8*a^6/(1/8)*8*a^6$ (multiplying by the denominators to eliminate the denominators)
$8/a^6$ (simplifying the expression)
