Final answer:
The expression d⁶df⁰ simplifies to d⁷ by applying the Laws of Exponents, which include adding exponents when multiplying like bases and recognizing that anything raised to the power of zero is one. The correct answer is option b.
Step-by-step explanation:
The task is to apply the Laws of Exponents to write an equivalent expression for the given expression d⁶df⁰. To solve this, we need to understand two exponent rules. First, when two exponential terms with the same base are multiplied together, the exponents are added.
Therefore, d⁶ * d becomes d^(6+1) or d⁷. The second rule to remember is that any number raised to the power of zero is one, thus f⁰ equals 1. Multiplying by 1 does not change the value of the other terms, so it does not appear in the simplified expression.
Using these rules, the given expression simplifies to d⁷, which corresponds to option b. So the correct option is b. d⁷.