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

Question

(1 point)
Responses

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

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

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

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

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

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

1.024×10−48

Answer 1

To simplify the expression \((4 \times 10^{-9})^5\), we can use the property of exponents \((a \times b)^n = a^n \times b^n\).

First, we handle the coefficient and then the exponent separately:

1. Coefficient Calculation: \[ 4^5 = 1024 \]

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

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

Next, we need to convert \(1024\) into scientific notation. Note that \(1024\) can be expressed as \(1.024 \times 10^3\) (since \(1024 = 1.024 \times 1000\)).

Now we substitute this back into our expression: \[ 1024 \times 10^{-45} = (1.024 \times 10^3) \times 10^{-45} \]

Using the property of exponents \(10^a \times 10^b = 10^{a + b}\), we combine the powers of ten: \[ 1.024 \times 10^{3 - 45} = 1.024 \times 10^{-42} \]

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