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

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

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

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

2.0×10−3

Answer 1

To simplify the expression \((4 \times 10^{-9})^5\), we can apply the power of a product rule.

1. **Apply the exponent to both parts of the product**:
\[
(4 \times 10^{-9})^5 = 4^5 \times (10^{-9})^5
\]

2. **Calculate \(4^5\)**:
\[
4^5 = 1024
\]

3. **Calculate \((10^{-9})^5\)**:
\[
(10^{-9})^5 = 10^{-45}
\]

4. **Combine the results**:
\[
1024 \times 10^{-45}
\]

5. **Convert \(1024\) to scientific notation**:
\[
1024 = 1.024 \times 10^3
\]

6. **Substituting back into the equation**:
\[
1024 \times 10^{-45} = (1.024 \times 10^3) \times 10^{-45}
\]

7. **Combine the powers of ten**:
\[
1.024 \times 10^{3 - 45} = 1.024 \times 10^{-42}
\]

So, the simplified expression in scientific notation is:

\(\boxed{1.024 \times 10^{-42}}\)