Question

Which expressions are equivalent to (4^)3(4d)3?

a) 3d3 ^3
b) 344d3 ^3
c) 1212d ^3
d) 444d4^3

Answer 1

To simplify the expression, we apply the rules of exponents and multiplication to find that it is equivalent to 4096d^3.

Step-by-step explanation:

In this case, the expression (4^3)(4d)^3 can be simplified by applying the rules of exponents and multiplication. Let's break it down step by step:

1. The first term, 4^3, means 4 raised to the power of 3, which is equivalent to 4 x 4 x 4 = 64.
2. The second term, (4d)^3 means (4d) raised to the power of 3. The exponent applies to both the 4 and the d separately. So, (4d) raised to the power of 3 is equal to (4^3)(d^3) = 64d^3.
3. Putting the two simplified terms together, we have 64 x 64d^3 = 4096d^3.

Therefore, the expression (4^3)(4d)^3 is equivalent to 4096d^3.