Final answer:
To simplify the expression (z⁵z³z²)⁵, first combine the exponents by addition to get z⁵⁰, then apply the power of a power rule to get the final simplified expression of z¹⁰²⁰.
Step-by-step explanation:
The question asks to simplify the expression (z⁵z³z²)⁵ using integer powers and write the answer with only positive exponents.
First, we need to combine the exponents in the base by adding them up, as per the rule for multiplying powers with the same base (when multiplying powers with the same base, you add the exponents). So, we have:
z⁵ × z³ × z² = z^(5+3+2) = z⁵⁰
Next, we apply the power of a power rule (to raise a power to a power, you multiply the exponents), hence:
(z⁵⁰)⁵ = z^(50×5) = z¹⁰²⁰
Therefore, the expression simplifies to z¹⁰²⁰ with only positive exponents.