Final answer:
The simplified expression for [(p^2)(q^5)]*[(p^-4)(q^5)]^-2 is p^10.
Step-by-step explanation:
To simplify the expression [(p^2)(q^5)]*[(p^-4)(q^5)]^-2, we can first simplify the expressions inside the parentheses.
(p^2)(q^5) = p^2 * q^5
(p^-4)(q^5) = p^-4 * q^5
Next, take the negative exponent of the second expression and reciprocate both the base and the exponent.
p^-4 = 1/(p^4).
Now substitute the simplified expressions back into the original expression:
[(p^2)(q^5)]*[(p^-4)(q^5)]^-2 = p^2 * q^5 * [1/(p^4) * q^5]^-2
Apply the rule that states that when we raise a fraction to a negative exponent, we can flip the fraction and make the exponent positive:
[1/(p^4) * q^5]^-2 = [(p^4)/q^5]^2
Now multiply the terms together:
p^2 * q^5 * [(p^4)/q^5]^2 = p^2 * (p^4)^2 = p^2 * p^8 = p^(2+8) = p^10
Therefore, the simplified expression is p^10.