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

Question

(1 point)
Responses

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

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

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

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

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

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

2.0×10−3

Answer 1

To simplify the expression \((4 \times 10^{-9})^5\), we can split it into two parts:

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

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

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

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

So, we can rewrite the expression: \[ 1024 \times 10^{-45} = (1.024 \times 10^3) \times 10^{-45} = 1.024 \times 10^{3 - 45} = 1.024 \times 10^{-42} \]

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