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

Question

(1 point)
Responses

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

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

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

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

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

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

2.0×10−3

Answer 1

To simplify the expression \((4 \times 10^{-9})^5\), we can apply the power of a product rule.

1. Apply the exponent to both parts of the product: \[ (4 \times 10^{-9})^5 = 4^5 \times (10^{-9})^5 \]

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

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

4. Combine the results: \[ 1024 \times 10^{-45} \]

5. Convert \(1024\) to scientific notation: \[ 1024 = 1.024 \times 10^3 \]

6. Substituting back into the equation: \[ 1024 \times 10^{-45} = (1.024 \times 10^3) \times 10^{-45} \]

7. Combine the powers of ten: \[ 1.024 \times 10^{3 - 45} = 1.024 \times 10^{-42} \]

So, the simplified expression in scientific notation is:

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