Question

Simplify the following expression to Scientific Notation: (4×10−9)5
(1 point)
Responses

20×10−4
20 times 10 to the negative 4 power

1.024×10−42
1 point 0 2 4 times 10 to the negative 42 power

4×10−20
4 times 10 to the negative 20 power

1.024×10−48
1 point 0 2 4 times 10 to the negative 48 power

2.0×10−46
2 point 0 times 10 to the negative 46 power

4×10−45
4 times 10 to the negative 45 power

2.0×10−3

Answer 1

To simplify the expression \((4 \times 10^{-9})^5\), we can use the properties of exponents.

1. **Raise the coefficient (4) to the power of 5**:
\[
4^5 = 1024
\]

2. **Raise the power of ten to the power of 5**:
\[
(10^{-9})^5 = 10^{-45}
\]

3. **Combine the results**:
\[
(4 \times 10^{-9})^5 = 1024 \times 10^{-45}
\]

Next, we need to express \(1024\) in scientific notation. \(1024\) can be rewritten as \(1.024 \times 10^3\). Therefore, we substitute this back into our expression:

\[
1024 \times 10^{-45} = (1.024 \times 10^3) \times 10^{-45} = 1.024 \times 10^{-42}
\]

So, the answer in scientific notation is:

\[
\boxed{1.024 \times 10^{-42}}
\]