Final answer:
The expression (7a⁻⁵)b³ is written with a positive exponent as (7b³)/(a⁵), taking the reciprocal of a to the negative fifth power and leaving the 7 and b cubed intact. The correct answer is option A.
Step-by-step explanation:
To write (7a⁻⁵)b³ as a positive exponent, we need to move the negative exponent to the denominator of the fraction. Since a⁻⁵ means 1/a⁵, we can rewrite the expression as (7/a⁵)b³. So the answer is (b³)/(7a⁵), which is option a.
To write (7a⁻⁵)b³ with a positive exponent, we will apply the rule that states when we have a negative exponent, the expression can be made positive by taking the reciprocal of that term. In this case, a⁻⁵ can be rewritten as 1/a⁻⁻⁵ or 1/(a⁵), and the 7 remains in its original position because it does not have an exponent. Hence, the correct rewrite of the expression is (7b³)/(a⁵), which corresponds to option b.
Remember, the rule (xa)b = xa.b implies that when raising a power to another power, you multiply the exponents. This is relevant when working with exponentiated quantities but does not apply directly to our initial expression, as we are not dealing with nested exponents. To write (7a⁻⁵)b³ as a positive exponent, we need to move the negative exponent to the denominator of the fraction. Since a⁻⁵ means 1/a⁵, we can rewrite the expression as (7/a⁵)b³. So the answer is (b³)/(7a⁵), which is option a.