Final answer:
The expression (2t)^-6 simplifies to 1/(64t^6) using positive exponents. The expression (w^-2j^-4)^-3(j^7j^3) simplifies to w^6j^22 considering the rules for multiplying and raising powers.
Step-by-step explanation:
To simplify the expression (2t)^-6 using only positive exponents, we apply the rule that a negative exponent indicates a reciprocal. Thus, (2t)^-6 is equivalent to 1/(2t)^6. To further simplify, raise both 2 and t to the 6th power, which gives 1/(64t^6).
For the second expression, (w^-2j^-4)^-3( j^7j^3), we apply several exponent rules. To begin with, when raising a power to a power, we multiply the exponents, so (w^-2j^-4)^-3 becomes w^6j^12. When multiplying exponents with the same base, we add the exponents, so j^7j^3 becomes j^(7+3) or j^10. Combining these results, we have w^6j^12 multiplied by j^10, which simplifies to w^6j^22.