Final answer:
The equivalent expression of (4^3)(4^6) is found by applying the power rule for exponents, simply adding the exponents with the same base resulting in 4^9. The correct answer is C.
Step-by-step explanation:
The student is asking to simplify the expression (4^3)(4^6). According to the properties of exponents, when we multiply two exponential expressions with the same base, we simply add their exponents. Therefore, the equivalent expression can be found by adding the exponents of 4 in the given expression.
The calculation would look like this:
4^3 × 4^6 = 4^{3+6}
= 4^9.
The use of the power rule for exponents, which states that a^m × a^n = a^{m+n}, simplifies the original expression to 4^9. This shows that we have effectively combined the exponents 3 and 6 to get 9. Hence the answer is C.