Question

Which of the following is an equivalent expression to 7 · (1 0.20)3x?

1) 7 · (1.728)x
2) 7 · (3.6)x
3) 343 · (1.2)x
4) 21 · (1.2)x

Answer 1

The equivalent expression to 7 · (1 + 0.20)^{3x} is 7 · (1.728)^x, which matches the first option provided.

Step-by-step explanation:

To determine which of the provided expressions is equivalent to 7 · (1 + 0.20)^{3x}, we can simplify the original expression step-by-step. First, we notice that (1 + 0.20) is the same as 1.2. Raising this to the power of 3x, we get (1.2^{3x}). According to exponent rules, powers can be multiplied when they are raised by another power, so (1.2^{3})^{x} simplifies further to (1.2^3)^x. Calculating 1.2 cubed (1.2 × 1.2 × 1.2) gives us approximately 1.728. Therefore, the expression simplifies to 7 · (1.728)^x or 7 · (1.728)^x.