Simplify the following expression to Scientific Notation: (4×10

Question

−9
)
5
(1 point)

1.024×10
−42

2.0×10
−3

20×10
−4

4×10
−45

2.0×10
−46

4×10
−20

1.024×10
−48

Answer 1

To simplify the expression \((4 \times 10^{-9})^5\), we can apply the properties of exponents. We can separate the numeric part and the power of ten:

\[ (4 \times 10^{-9})^5 = 4^5 \times (10^{-9})^5 \]

Now calculate each part:

1. Calculate \(4^5\):

\[ 4^5 = 1024 \]

2. Calculate \((10^{-9})^5\):

\[ (10^{-9})^5 = 10^{-45} \]

Now combine the results:

\[ 1024 \times 10^{-45} \]

Next, we need to express \(1024\) in scientific notation. \(1024\) can be written as \(1.024 \times 10^3\).

Now substitute back into the expression:

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

Now combine the powers of ten:

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

Thus, the simplified expression in scientific notation is:

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

So, the correct answer is:

1.024 × 10^{-42}