Question

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

Answer 1

To simplify the expression \((4 \times 10^{-9})^5\), we can apply the power to both the coefficient and the power of ten separately.

1. First, we calculate the coefficient:
\[
4^5 = 1024
\]

2. Next, we apply the exponent to the power of ten:
\[
(10^{-9})^5 = 10^{-9 \times 5} = 10^{-45}
\]

3. Now we combine both results:
\[
(4 \times 10^{-9})^5 = 1024 \times 10^{-45}
\]

Since \(1024\) is not in scientific notation, we need to express it in the correct format. In scientific notation, \(1024\) can be written as:
\[
1.024 \times 10^3
\]

4. Now we multiply this by \(10^{-45}\):
\[
1.024 \times 10^3 \times 10^{-45} = 1.024 \times 10^{3 - 45} = 1.024 \times 10^{-42}
\]

Thus, the final result in scientific notation is:
\[
\boxed{1.024 \times 10^{-42}}
\]