Final answer:
The given expression ((a²)⁻²)⁵/(a⁴*a)³ simplifies to a to the power of -35 by following the laws of exponents, namely the product of powers rule and the power of a power rule.
Step-by-step explanation:
To represent the given expression ((a²)⁻²)⁵/(a⁴*a)³ as a power of a where a doesn't equal 0, we need to apply the rules of exponents. Firstly, we simplify the numerator (((a²)⁻²)⁵) by multiplying the exponents which gives us a to the power of -20. Then, we simplify the denominator ((a⁴*a)³) by first combining the a's to a⁵ before raising it to the power of 3 which gives us a to the power of 15. Dividing exponents with the same base means subtracting their powers, so we get a to the power of -20 minus 15, which equals a to the power of -35.
In summary, following the rules for exponents and division of powers, the given expression can be represented as a⁻³⁵.