Question

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

1.024×10−481 point 0 2 4 times 10 to the negative 48 power

2.0×10−32 point 0 times 10 to the negative 3 power

4×10−204 times 10 to the negative 20 power

2.0×10−462 point 0 times 10 to the negative 46 power

4×10−454 times 10 to the negative 45 power

20×10−420 times 10 to the negative 4 power

1.024×10^−42

Answer 1

To simplify the expression \((4 \times 10^{-9})^5\), we need to apply the power rule for exponents.

First, we simplify the coefficient:
\[
4^5 = 1024
\]

Next, we simplify the powers of ten:
\[
(10^{-9})^5 = 10^{-45}
\]

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

We want to express \(1024\) in scientific notation:
\[
1024 = 1.024 \times 10^3
\]

Now, substitute this back into the expression:
\[
1.024 \times 10^3 \times 10^{-45}
\]

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

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