Question

Simplify the following expression to Scientific Notation:  (4×10^−9)^5 (1 point)Responses20×10−420 times 10 to the negative 4 power1.024×10−421 point 0 2 4 times 10 to the negative 42 power2.0×10−462 point 0 times 10 to the negative 46 power4×10−204 times 10 to the negative 20 power2.0×10−32 point 0 times 10 to the negative 3 power1.024×10−481 point 0 2 4 times 10 to the negative 48 power4×10−45

Answer 1

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

1. Raise the coefficient:
\[
4^5 = 1024
\]

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

Combining these results, we get:
\[
(4 \times 10^{-9})^5 = 1024 \times 10^{-45}
\]

Now, we convert \(1024\) into scientific notation. Since \(1024 = 1.024 \times 10^3\), we can write:
\[
1024 \times 10^{-45} = 1.024 \times 10^3 \times 10^{-45}
\]

Now, we combine the powers of 10:
\[
1.024 \times 10^{3 - 45} = 1.024 \times 10^{-42}
\]

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